Relevant bibliographies by topics / Wave equation – Numerical solutions

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Wave equation – Numerical solutions'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Wave equation – Numerical solutions"

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Zhang, Yingnan, Xingbiao Hu, and Jianqing Sun. "Numerical calculation of N -periodic wave solutions to coupled KdV–Toda-type equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2245 (2021): 20200752. http://dx.doi.org/10.1098/rspa.2020.0752.

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In this paper, we study the N -periodic wave solutions of coupled Korteweg–de Vries (KdV)–Toda-type equations. We present a numerical process to calculate the N -periodic waves based on the direct method of calculating periodic wave solutions proposed by Akira Nakamura. Particularly, in the case of N = 3, we give some detailed examples to show the N -periodic wave solutions to the coupled Ramani equation, the Hirota–Satsuma coupled KdV equation, the coupled Ito equation, the Blaszak–Marciniak lattice, the semi-discrete KdV equation, the Leznov lattice and a relativistic Toda lattice.
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HIKIHARA, TAKASHI, KENTARO TORII, and YOSHISUKE UEDA. "WAVE AND BASIN STRUCTURE IN SPATIALLY COUPLED MAGNETO-ELASTIC BEAM SYSTEM — TRANSITIONS BETWEEN COEXISTING WAVE SOLUTIONS." International Journal of Bifurcation and Chaos 11, no. 04 (2001): 999–1018. http://dx.doi.org/10.1142/s0218127401002523.

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Standing and traveling waves are well-known phenomena of the coupled ordinary differential equations in many fields. The wave solutions of the coupled system are considered to be similar to the partial differential equation of the system. In this paper, the waves which appear in a coupled magneto-elastic beam system are discussed theoretically and numerically. The physical system is continuous elastically and discrete magnetically. There are several classes of models describing the system behavior. The Galerkin method is one of the powerful methods used to analyze the dynamics of the spatially distributed structure. The numerical solutions appearing in the coupled ordinary differential equation must show the spatially discrete characteristics even in the distributed system. However, most of the results obtained in the coupled systems are not more than the numerical approximation of the related partial differential equations. The large number of oscillators are given for the approximation. In this paper, the relationship between the coupled magneto-elastic beam system and the modified KdV equation is established by using the long wave approximation. However, in the short wavelength range, the approximation to the partial differential equation has no physical rationality. Therefore, the analysis of the difference–differential equation provides an important place of knowledge filling up the gap between the characteristics of the physical model and the numerical approximation.
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Alkhalifah, Tariq. "An acoustic wave equation for anisotropic media." GEOPHYSICS 65, no. 4 (2000): 1239–50. http://dx.doi.org/10.1190/1.1444815.

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A wave equation, derived using the acoustic medium assumption for P-waves in transversely isotropic (TI) media with a vertical symmetry axis (VTI media), yields a good kinematic approximation to the familiar elastic wave equation for VTI media. The wavefield solutions obtained using this VTI acoustic wave equation are free of shear waves, which significantly reduces the computation time compared to the elastic wavefield solutions for exploding‐reflector type applications. From this VTI acoustic wave equation, the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a TI medium are derived. These equations, based on the acoustic assumption (shear wave velocity = 0), are much simpler than their elastic counterparts, yet they yield an accurate description of traveltimes and geometrical amplitudes. Numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex TI models.
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Yokuş, Asıf, and Doğan Kaya. "Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics." International Journal of Modern Physics B 34, no. 29 (2020): 2050282. http://dx.doi.org/10.1142/s0217979220502823.

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The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Bäcklund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier–von Neumann stability analysis, the stability of the FDM with the cKdV–mKdV equation is analyzed. The [Formula: see text] and [Formula: see text] norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.
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Cai, Wenjun, Yajuan Sun, and Yushun Wang. "Geometric Numerical Integration for Peakon b-Family Equations." Communications in Computational Physics 19, no. 1 (2016): 24–52. http://dx.doi.org/10.4208/cicp.171114.140715a.

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AbstractIn this paper, we study the Camassa-Holm equation and the Degasperis-Procesi equation. The two equations are in the family of integrable peakon equations, and both have very rich geometric properties. Based on these geometric structures, we construct the geometric numerical integrators for simulating their soliton solutions. The Camassa-Holm equation and the Degasperis-Procesi equation have many common properties, however they also have the significant difference, for example there exist the shock wave solutions for the Degasperis-Procesi equation. By using the symplectic Fourier pseudo-spectral integrator, we simulate the peakon solutions of the two equations. To illustrate the smooth solitons and shock wave solutions of the DP equation, we use the splitting technique and combine the composition methods. In the numerical experiments, comparisons of these two kinds of methods are presented in terms of accuracy, computational cost and invariants preservation.
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Kay, Alison L., Jonathan A. Sherratt, and J. B. McLeod. "Comparison theorems and variable speed waves for a scalar reaction–diffusion equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 5 (2001): 1133–61. http://dx.doi.org/10.1017/s030821050000130x.

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This paper concerns the reaction-diffusion equation ut = uxx + u2(1 − u). Previous numerical solutions of this equation have demonstrated various different types of wave front solutions, generated by different initial conditions. In this paper, the authors use a phase-plane form of comparison theorems for partial differential equations (PDEs) to confirm analytically these numerical results. In particular, they show that initial conditions with an exponentially decaying tail evolve to the unique exponentially decaying travelling wave, while initial conditions with algebraically decaying tails evolve either to an algebraically decaying travelling wave, or to the exponentially decaying wave, or to a perpetually accelerating wave, dependent upon the exact form of the decay of the initial conditions. We then focus on the case of accelerating waves and investigate their form in more detail, by approximating the full equation in this case with a hyperbolic PDE, which we solve using the method of characteristics. We use this approximate solution to derive a leading-order approximation to the wave speed.
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AMORIM, PAULO, and MÁRIO FIGUEIRA. "CONVERGENCE OF NUMERICAL SCHEMES FOR SHORT WAVE LONG WAVE INTERACTION EQUATIONS." Journal of Hyperbolic Differential Equations 08, no. 04 (2011): 777–811. http://dx.doi.org/10.1142/s0219891611002573.

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We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schrödinger equation coupled with a hyperbolic conservation law. This system arises in models for the interaction of short and long waves. Using the compensated compactness method, we prove convergence of approximate solutions generated by semi-discrete finite volume type methods towards the unique entropy solution of the Cauchy problem. Some numerical examples are presented.
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Alharbi, Abdulghani R., M. B. Almatrafi, and Aly R. Seadawy. "Construction of the numerical and analytical wave solutions of the Joseph–Egri dynamical equation for the long waves in nonlinear dispersive systems." International Journal of Modern Physics B 34, no. 30 (2020): 2050289. http://dx.doi.org/10.1142/s0217979220502896.

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The Kudryashov technique is employed to extract several classes of solitary wave solutions for the Joseph–Egri equation. The stability of the achieved solutions is tested. The numerical solution of this equation is also investigated. We also present the accuracy and the stability of the numerical schemes. Some two- and three-dimensional figures are shown to present the solutions on some specific domains. The used methods are found useful to be applied on other nonlinear evolution equations.
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Zhang, X., X. X. Chen, and C. L. Morfey. "Acoustic Radiation from a Semi-Infinite Duct With a Subsonic Jet." International Journal of Aeroacoustics 4, no. 1-2 (2005): 169–84. http://dx.doi.org/10.1260/1475472053730075.

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The radiation of high-order spinning modes from a semi-infinite exhaust duct is studied numerically. The issues involved have applications to noise radiation from the exhaust duct of an aircraft engine. The numerical method is based on solutions of linearised Euler equations (LEE) for propagation in the duct and near field, and the acoustic analogy for far field radiation. A 2.5D formulation of a linearised Euler equation model is employed to accommodate a single spinning mode propagating over an axisymmetric mean flow field. In the solution process, acoustic waves are admitted into the propagation area surrounding the exit of an axisymmetric duct and its immediate downstream area. The wave admission is realised through an absorbing non-reflecting boundary treatment, which admits incoming waves and damps spurious waves generated by the numerical solutions. The wave propagation is calculated through solutions of linearised Euler equations, using an optimised prefactored compact scheme for spatial discretisation. Far field directivity is estimated by solving the Ffowcs Williams-Hawkings equations. The far field prediction is compared with analytic solutions with good agreement.
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Özkan, Yeşim Sağlam, Emrullah Yaşar, and Nisa Çelik. "On the exact and numerical solutions to a new (2 + 1)-dimensional Korteweg-de Vries equation with conformable derivative." Nonlinear Engineering 10, no. 1 (2021): 46–65. http://dx.doi.org/10.1515/nleng-2021-0005.

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Abstract The aim of this paper is to introduce a novel study of obtaining exact solutions to the (2+1) - dimensional conformable KdV equation modeling the amplitude of the shallow-water waves in fluids or electrostatic wave potential in plasmas. The reduction of the governing equation to a simpler ordinary differential equation by wave transformation is the first step of the procedure. By using the improved tan(φ/2)-expansion method (ITEM) and Jacobi elliptic function expansion method, exact solutions including the hyperbolic function solution, rational function solution, soliton solution, traveling wave solution, and periodic wave solution of the considered equation have been obtained. We achieve also a numerical solution corresponding to the initial value problem by conformable variational iteration method (C-VIM) and give comparative results in tables. Moreover, by using Maple, some graphical simulations are done to see the behavior of these solutions with choosing the suitable parameters.
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Dissertations / Theses on the topic "Wave equation – Numerical solutions"

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Sundström, Carl. "Numerical solutions to high frequency approximations of the scalar wave equation." Thesis, Uppsala universitet, Tillämpad beräkningsvetenskap, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-429072.

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Throughout many fields of science and engineering, the need for describing waveequations is crucial. Solving the wave equation for high-frequency waves istime-consuming, requires a fine mesh size and memory usage. The main goal wasimplementing and comparing different solution methods for high-frequency waves.Four different methods have been implemented and compared in terms of runtimeand discretization error. From my results, the method which performs the best is thefast sweeping method. For the fast marching method, the time-complexity of thenumerical solver was higher than expected which indicates an error in myimplementation.
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Huang, Jeffrey. "Numerical solutions of continuous wave beam in nonlinear media." PDXScholar, 1987. https://pdxscholar.library.pdx.edu/open_access_etds/3742.

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Deformation of a Gaussian beam is observed when it propagates through a plasma. Self-focusing of the beam may be observed when the intensity of the laser increases the index of refraction of plasma gas. Due to the difficulties in solving the nonlinear partial differential equation in Maxwell's wave equation, a numerical technique has been developed in favor of the traditional analytical method. Result of numerical solution shows consistency with the analytical method. This further suggests the validity of the numerical technique employed. A three dimensional graphics package was used to depict the numerical data obtained from the calculation. Plots from the data further show the deformation of the Gaussian beam as it propagates through the plasma gas.
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Koutoumbas, Anastasios M. "Bidirectional and unidirectional spectral representations for the scalar wave equation." Thesis, Virginia Tech, 1990. http://hdl.handle.net/10919/41904.

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<p>The Cauchy problem associated with the scalar wave equation in free space is used as a vehicle for a critical examination and assessment of the bidirectional and unidirectional spectral representations. These two novel methods for synthesizing wave signals are distinct from the superposition principle underlying the conventional Fourier method and they can effectively be used to derive a large class of localized solutions to the scalar wave equation. The bidirectional spectral representation is presented as an extension of Brittingham's ansatz and Ziolkowski's Focus Wave Mode spectral representations. On the other hand, the unidirectional spectral representation is motivated through a group-theoretic similarity reduction of the scalar wave equation.</p><br>Master of Science
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Agiza, Hamdy N. "A numerical and theoretical study of solutions to a damped nonlinear wave equation." Thesis, Heriot-Watt University, 1987. http://hdl.handle.net/10399/1058.

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Li, Hongwei. "Local absorbing boundary conditions for wave propagations." HKBU Institutional Repository, 2012. https://repository.hkbu.edu.hk/etd_ra/1434.

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Pack, Jeong-Ki. "A wave-kinetic numerical method for the propagation of optical waves." Thesis, Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/104527.

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Meral, Gulnihal. "Numerical Solution Of Nonlinear Reaction-diffusion And Wave Equations." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/3/12610568/index.pdf.

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In this thesis, the two-dimensional initial and boundary value problems (IBVPs) and the one-dimensional Cauchy problems defined by the nonlinear reaction- diffusion and wave equations are numerically solved. The dual reciprocity boundary element method (DRBEM) is used to discretize the IBVPs defined by single and system of nonlinear reaction-diffusion equations and nonlinear wave equation, spatially. The advantage of DRBEM for the exterior regions is made use of for the latter problem. The differential quadrature method (DQM) is used for the spatial discretization of IBVPs and Cauchy problems defined by the nonlinear reaction-diffusion and wave equations. The DRBEM and DQM applications result in first and second order system of ordinary differential equations in time. These systems are solved with three different time integration methods, the finite difference method (FDM), the least squares method (LSM) and the finite element method (FEM) and comparisons among the methods are made. In the FDM a relaxation parameter is used to smooth the solution between the consecutive time levels. It is found that DRBEM+FEM procedure gives better accuracy for the IBVPs defined by nonlinear reaction-diffusion equation. The DRBEM+LSM procedure with exponential and rational radial basis functions is found suitable for exterior wave problem. The same result is also valid when DQM is used for space discretization instead of DRBEM for Cauchy and IBVPs defined by nonlinear reaction-diffusion and wave equations.
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Lampshire, Gregory B. "Review of random media homogenization using effective medium theories." Thesis, Virginia Tech, 1992. http://hdl.handle.net/10919/40659.

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<p>Calculation of propagation constants in particulate matter is an important aspect of wave propagation analysis in engineering disciplines such as satellite comnlunication, geophysical exploration, radio astronomy and material science. It is important to understand why different propagation constants produced by different theories are not applicable to a particular problem. Homogenization of the random media using effective medium theories yields the effective propagation constants by effacing the particulate, microscopic nature of the medium. The Maxwell-Gamet and Bruggeman effective medium theories are widely used but their limitations are not always well understood.</p> <p> In this thesis, some of the more complex homogenization theories will only be partially derived or heuristically constructed in order to avoid unnecessary mathematical complexity which does not yield additional physical insight. The intent of this thesis is to elucidate the nature of effective medium theories, discuss the theories' approximations and gain a better global understanding of wave propagation equations. The focus will be on the Maxwell-Garnet and Bruggeman theories because they yield simple relationships and therefore serve as anchors in a sea of myriad approximations.</p><br>Master of Science
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Sugimoto, Rie. "Special wave finite and infinite elements for the solution of the Helmholtz equation." Thesis, Durham University, 2003. http://etheses.dur.ac.uk/3142/.

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The theory and the formulation of the special wave finite elements are discussed, and the special integration schemes for the elements are developed. Then the special wave infinite elements, a new concept of the mapped wave infinite elements with multiple wave directions, are developed. Computational models using these elements coupled together are tested by the applications of wave problems. In the special wave finite elements, the potential at each node is expanded in a discrete series of approximating plane waves propagating in different directions. Because of this a single element can contain many wavelengths, unlike the standard finite elements. This is a great advantage in the reduction of the degree of freedom of the problem, however the computational cost of the numerical integration over an element becomes high due to the oscillatory shape functions. Therefore the special semi-analytical integration schemes for the special wave finite elements are developed. The schemes are independent of wavenumber and efficient for short waves problems. In many cases of wave problems, it is practical to consider the domain as being infinite. However the finite element method can not deal with infinite domains. Infinite elements are an extension of the concept of finite elements in which the element has an infinite extent in one or more directions to address this limitation. In the special wave infinite element developed in this study multiple waves propagating in different directions are considered, in contrast to conventional infinite elements in which only a single wave propagating in the radial direction is considered. The shape functions of the special wave infinite elements contain trigonometric functions to describe multiple waves, and the amplitude decay factor to satisfy the radiation condition. The special wave infinite elements become a straightforward extension to the special wave finite elements for wave problems in an unbounded domain.
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Pinilla, Camilo Ernesto. "Numerical simulation of shear instability in shallow shear flows." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115697.

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The instabilities of shallow shear flows are analyzed to study exchanges processes across shear flows in inland and coastal waters, coastal and ocean currents, and winds across the thermal-and-moisture fronts. These shear flows observed in nature are driven by gravity and governed by the shallow water equations (SWE). A highly accurate, and robust, computational scheme has been developed to solve these SWE. Time integration of the SWE was carried out using the fourth-order Runge-Kutta scheme. A third-order upwind bias finite difference approximation known as QUICK (Quadratic Upstream Interpolation of Convective Kinematics) was employed for the spatial discretization. The numerical oscillations were controlled using flux limiters for Total Variation Diminishing (TVD). Direct numerical simulations (DNS) were conducted for the base flow with the TANH velocity profile, and the base flow in the form of a jet with the SECH velocity profile. The depth across the base flows was selected for the' balance of the driving forces. In the rotating flow simulation, the Coriolis force in the lateral direction was perfectly in balance with the pressure gradient across the shear flow during the simulation. The development of instabilities in the shear flows was considered for a range of convective Froude number, friction number, and Rossby number. The DNS of the SWE has produced linear results that are consistent with classical stability analyses based on the normal mode approach, and new results that had not been determined by the classical method. The formation of eddies, and the generation of shocklets subsequent to the linear instabilities were computed as part of the DNS. Without modelling the small scales, the simulation was able to produce the correct turbulent spreading rate in agreement with the experimental observations. The simulations have identified radiation damping, in addition to friction damping, as a primary factor of influence on the instability of the shear flows admissible to waves. A convective Froude number correlated the energy lost due to radiation damping. The friction number determined the energy lost due to friction. A significant fraction of available energy produced by the shear flow is lost due the radiation of waves at high convective Froude number. This radiation of gravity waves in shallow gravity-stratified shear flow, and its dependence on the convective Froude number, is shown to be analogous to the Mach-number effect in compressible flow. Furthermore, and most significantly, is the discovery from the simulation the crucial role of the radiation damping in the development of shear flows in the rotating earth. Rings and eddies were produced by the rotating-flow simulations in a range of Rossby numbers, as they were observed in the Gulf Stream of the Atlantic, Jet Stream in the atmosphere, and various fronts across currents in coastal waters.
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Books on the topic "Wave equation – Numerical solutions"

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Nonlinear dispersive equations: Existence and stability of solitary and periodic travelling wave solutions. American Mathematical Society, 2009.

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Pava, Jaime Angulo. Nonlinear dispersive equations: Existence and stability of solitary and periodic travelling wave solutions. American Mathematical Society, 2009.

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Pava, Jaime Angulo. Nonlinear dispersive equations: Existence and stability of solitary and periodic travelling wave solutions. American Mathematical Society, 2009.

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Pava, Jaime Angulo. Nonlinear dispersive equations: Existence and stability of solitary and periodic travelling wave solutions. American Mathematical Society, 2009.

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Haraux, Alain. Nonlinear vibrations and the wave equation. Universidade Federal do Rio de Janeiro, Centro de Ciências Matemáticas e da Natureza, Instituto de Matemática, 1986.

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Bagrov, V. G. Exact solutions of relativistic wave equations. Kluwer Academic Publishers, 1990.

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Pava, Jaime Angulo. Nonlinear dispersive equations: Existence and stability of solitary and periodic travelling waves solutions. American Mathematical Society, 2009.

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Robertsson, Johan O. A. Numerical modeling of seismic wave propagation: Gridded two-way wave-equation methods. Society of Exploration Geophysicists, the international society of applied geophysics, 2012.

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Nonlinear waves in integrable and nonintegrable systems. Society for Industrial and Applied Mathematics, 2010.

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Pava, Jaime Angulo. Nonlinear dispersive equations: Existence and stability of solitary and periodic travelling wave solutions. American Mathematical Society, 2009.

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Book chapters on the topic "Wave equation – Numerical solutions"

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Balabane, Mikhaël. "Computing Solutions for Helmholtz Equation: Domain Versus Boundary Decomposition." In Mathematical and Numerical Aspects of Wave Propagation WAVES 2003. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55856-6_2.

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Glowinski, Roland, Jacques Periaux, and Jari Toivanen. "Time-Periodic Solutions of Wave Equation via Controllability and Fictitious Domain Methods." In Mathematical and Numerical Aspects of Wave Propagation WAVES 2003. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55856-6_131.

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Hagstrom, Thomas. "Numerical Experiments on a Nonlinear Wave Equation with Singular Solutions." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65870-4_34.

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Caldwell, J. "Numerical Solution of a Model Nonlinear Wave Equation." In Industrial Vibration Modelling. Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-4480-0_17.

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Baskonus, Haci Mehmet, Ajay Kumar, M. S. Rawat, Bilgin Senel, Gulnur Yel, and Mine Senel. "Studying on the Complex and Mixed Dark-Bright Travelling Wave Solutions of the Generalized KP-BBM Equation." In Advanced Numerical Methods for Differential Equations. CRC Press, 2021. http://dx.doi.org/10.1201/9781003097938-2.

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Fortes, C. J. E. M., J. L. M. Fernandes, and M. A. Vaz dos Santos. "A Finite Element Method for the Solution of a Time-Dependent Nonlinear Wave Propagation Equation." In Mathematical and Numerical Aspects of Wave Propagation WAVES 2003. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55856-6_110.

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Boubendir, Y., and A. Bendali. "Dealing with Cross-Points in a Non-Overlapping Domain Decomposition Solution of the Helmholtz Equation." In Mathematical and Numerical Aspects of Wave Propagation WAVES 2003. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55856-6_51.

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Beilina, Larisa, and V. Ruas. "Convergence of Explicit $$P_1$$ Finite-Element Solutions to Maxwell’s Equations." In Mathematical and Numerical Approaches for Multi-Wave Inverse Problems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48634-1_7.

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Shirikyan, Armen, and Leonid Volevich. "Asymptotic Properties of Solutions to High-Order Hyperbolic Equations Generalizing the Damped Wave Equation." In Hyperbolic Problems: Theory, Numerics, Applications. Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8724-3_39.

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Osborne, A. R., and E. Segré. "Numerical Construction of Nonlinear Wave Train Solutions of the Periodic Korteweg-de Vries Equation." In Inverse Problems and Theoretical Imaging. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-75298-8_59.

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Conference papers on the topic "Wave equation – Numerical solutions"

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Gurefe, Yusuf, and Emine Misirli. "Traveling wave solutions by extended trial equation method." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825911.

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Chen, Huaitang, Huicheng Yin, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "New Travelling Solitary Wave and Periodic Solutions of the Generalized Kawahara Equation." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790089.

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Bruzón, M. S., M. L. Gandarias, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Travelling Wave Solutions of the K(m, n) Equation with Generalized Evolution." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241438.

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Liu, Changfu, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Exact Periodic Solitary Wave Solutions and Propagation for the Potential Kadomtsev-Petviashvili Equation." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241573.

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Andrianov, Igor, Vladimir Bolshakov, Yuriy Kirichek, et al. "Periodical Solutions of Certain Strongly Nonlinear Wave Equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636758.

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Kazakov, A. L., and L. F. Spevak. "Numerical study of travelling wave type solutions for the nonlinear heat equation." In MECHANICS, RESOURCE AND DIAGNOSTICS OF MATERIALS AND STRUCTURES (MRDMS-2019): Proceedings of the 13th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5135130.

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Park, Joonsang, Karin Norén-Cosgriff, and Amir M. Kaynia. "NUMERICAL WAVENUMBER INTEGRATION FOR 2.5D WAVE EQUATION SOLUTION." In XI International Conference on Structural Dynamics. EASD, 2020. http://dx.doi.org/10.47964/1120.9239.19610.

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Shibata, Daisuke, and Takayuki Utsumi. "Numerical Solutions of Poisson Equation by the CIP-Basis Set Method." In ASME 2009 InterPACK Conference collocated with the ASME 2009 Summer Heat Transfer Conference and the ASME 2009 3rd International Conference on Energy Sustainability. ASMEDC, 2009. http://dx.doi.org/10.1115/interpack2009-89150.

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An accurate and reliable real space method for the ab initio calculation of electronic-structures of materials has been desired. Historically, the most popular method in this field has been the Plane Wave method. However, because the basis functions of the Plane Wave method are not local in real space, it is inefficient to represent the highly localized inner-shell electron state and it generally give rise to a large dense potential matrix which is difficult to deal with. Moreover, it is not suitable for parallel computers, because it requires Fourier transformations. These limitations of the Plane Wave method have led to the development of various real space methods including finite difference method and finite element method, and studies are still in progress. Recently, we have proposed a new numerical method, the CIP-Basis Set (CIP-BS) method [1], by generalizing the concept of the Constrained Interpolation Profile (CIP) method from the viewpoint of the basis set. This method uses a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. The interpolating profile is chosen so that the sub-grid scale solution approaches the local real solution by the constraints from the spatial derivative of the original equation. Thus the solution even on the sub-grid scale becomes consistent with the master equation. By increasing the order of the polynomial, this solution quickly converges. The governing equations are unambiguously discretized into matrix form equations requiring the residuals to be orthogonal to the basis functions via the same procedure as the Galerkin method. We have already demonstrated that the method can be applied to calculations of the band structures for crystals with pseudopotentials. It has been certified that the method gives accurate solutions in the very coarse meshes and the errors converge rapidly when meshes are refined. Although, we have dealt with problems in which potentials are represented analytically, in Kohn-Sham equation the potential is obtained by solving Poisson equation, where the charge density is determined by using wave functions. In this paper, we present the CIP-BS method gives accurate solutions for Poisson equation. Therefore, we believe that the method would be a promising method for solving self-consistent eigenvalue problems in real space.
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Liu, Changfu, Yanke Wu, and Bingtao Wei. "Construction of the multi-wave solutions for nonlinear evolution equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756676.

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Nečasová, Gabriela, Václav Šátek, and Jiří Kunovský. "Numerical solution of wave equation using higher order methods." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043964.

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Reports on the topic "Wave equation – Numerical solutions"

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Ghatak, A. K., R. L. Gallawa, and I. C. Goyal. Modified airy function and WKB solutions to the wave equation. National Institute of Standards and Technology, 1991. http://dx.doi.org/10.6028/nist.mono.176.

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Chang, B. Analytical Solutions for Testing Ray-Effect Errors in Numerical Solutions of the Transport Equation. Office of Scientific and Technical Information (OSTI), 2003. http://dx.doi.org/10.2172/15004539.

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Huang, Jeffrey. Numerical solutions of continuous wave beam in nonlinear media. Portland State University Library, 2000. http://dx.doi.org/10.15760/etd.5626.

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Hereman, W., P. P. Banerjee, and D. Faker. Construction of Solitary Wave Solutions of the Korteweg-De-Vries Equation Via Painleve Analysis. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada204101.

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Mickens, Ronald, and Kale Oyedeji. Exponential and Separation of Variables Exact Solutions to the Linear, Delayed, Unidirectional Wave Equation. Atlanta University Center Robert W. Woodruff Library, 2019. http://dx.doi.org/10.22595/cau.ir:2020_mickens_oyedeji_exponential.

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Arminjon, Mayeul. Classical-Quantum Correspondence and Wave Packet Solutions of the Dirac Equation In a Curved Space-Time. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-24-2011-77-88.

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Arminjon, Mayeul. Classical-Quantum Correspondence and Wave Packet Solutions of the Dirac Equation in a Curved Space-Time. GIQ, 2012. http://dx.doi.org/10.7546/giq-13-2012-96-106.

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Muhlestein, Michael, and Carl Hart. Numerical analysis of weak acoustic shocks in aperiodic array of rigid scatterers. Engineer Research and Development Center (U.S.), 2020. http://dx.doi.org/10.21079/11681/38579.

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Nonlinear propagation of shock waves through periodic structures have the potential to exhibit interesting phenomena. Frequency content of the shock that lies within a bandgap of the periodic structure is strongly attenuated, but nonlinear frequency-frequency interactions pumps energy back into those bands. To investigate the relative importance of these propagation phenomena, numerical experiments using the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation are carried out. Two-dimensional propagation through a periodic array of rectangular waveguides is per-formed by iteratively using the output of one waveguide as the input for the next waveguide. Comparison of the evolution of the initial shock wave for both the linear and nonlinear cases is presented.
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