Relevant bibliographies by topics / Parabolic Numerical solutions

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

Academic literature on the topic 'Parabolic Numerical solutions'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Parabolic Numerical solutions"

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Cannon, John R., and Hong-Ming Yin. "Numerical solutions of some parabolic inverse problems." Numerical Methods for Partial Differential Equations 6, no. 2 (1990): 177–91. http://dx.doi.org/10.1002/num.1690060207.

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FLOURI, EVANGELIA T., JOHN A. EKATERINARIS, and NIKOLAOS A. KAMPANIS. "HIGH-ORDER ACCURATE NUMERICAL SCHEMES FOR THE PARABOLIC EQUATION." Journal of Computational Acoustics 13, no. 04 (December 2005): 613–39. http://dx.doi.org/10.1142/s0218396x05002888.

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Efficient, high-order accurate methods for the numerical solution of the standard (narrow-angle) parabolic equation for underwater sound propagation are developed. Explicit and implicit numerical schemes, which are second- or higher-order accurate in time-like marching and fourth-order accurate in the space-like direction are presented. The explicit schemes have severe stability limitations and some of the proposed high-order accurate implicit methods were found conditionally stable. The efficiency and accuracy of various numerical methods are evaluated for Cartesian-type meshes. The standard parabolic equation is transformed to body fitted curvilinear coordinates. An unconditionally stable, implicit finite-difference scheme is used for numerical solutions in complex domains with deformed meshes. Simple boundary conditions are used and the accuracy of the numerical solutions is evaluated by comparing with an exact solution. Numerical solutions in complex domains obtained with a finite element method show excellent agreement with results obtained with the proposed finite difference methods.
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Choudhury, A. H. "Wavelet Method for Numerical Solution of Parabolic Equations." Journal of Computational Engineering 2014 (February 27, 2014): 1–12. http://dx.doi.org/10.1155/2014/346731.

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We derive a highly accurate numerical method for the solution of parabolic partial differential equations in one space dimension using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method using some special types of basis functions obtained by integrating Daubechies functions which are compactly supported and differentiable. The time variable is discretized by using various classical finite difference schemes. Theoretical and numerical results are obtained for problems of diffusion, diffusion-reaction, convection-diffusion, and convection-diffusion-reaction with Dirichlet, mixed, and Neumann boundary conditions. The computed solutions are highly favourable as compared to the exact solutions.
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Al-Sultani, Mohamed Saleh Mehdi, and Igor Boglaev. "Block monotone iterations for solving coupled systems of nonlinear parabolic equations." ANZIAM Journal 61 (July 28, 2020): C166—C180. http://dx.doi.org/10.21914/anziamj.v61i0.15144.

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The article deals with numerical methods for solving a coupled system of nonlinear parabolic problems, where reaction functions are quasi-monotone nondecreasing. We employ block monotone iterative methods based on the Jacobi and Gauss–Seidel methods incorporated with the upper and lower solutions method. A convergence analysis and the theorem on uniqueness of a solution are discussed. Numerical experiments are presented. References Al-Sultani, M. and Boglaev, I. ''Numerical solution of nonlinear elliptic systems by block monotone iterations''. ANZIAM J. 60:C79–C94, 2019. doi:10.21914/anziamj.v60i0.13986 Al-Sultani, M. ''Numerical solution of nonlinear parabolic systems by block monotone iterations''. Tech. Report, 2019. https://arxiv.org/abs/1905.03599 Boglaev, I. ''Inexact block monotone methods for solving nonlinear elliptic problems'' J. Comput. Appl. Math. 269:109–117, 2014. doi:10.1016/j.cam.2014.03.029 Lui, S. H. ''On monotone iteration and Schwarz methods for nonlinear parabolic PDEs''. J. Comput. Appl. Math. 161:449–468, 2003. doi:doi.org/10.1016/j.cam.2003.06.001 Pao, C. V. Nonlinear parabolic and elliptic equations. Plenum Press, New York, 1992. doi:10.1007/s002110050168 Pao C. V. ''Numerical analysis of coupled systems of nonlinear parabolic equations''. SIAM J. Numer. Anal. 36:393–416, 1999. doi:10.1137/S0036142996313166 Varga, R. S. Matrix iterative analysis. Springer, Berlin, 2000. 10.1007/978-3-642-05156-2 Zhao, Y. Numerical solutions of nonlinear parabolic problems using combined-block iterative methods. Masters Thesis, University of North Carolina, 2003. http://dl.uncw.edu/Etd/2003/zhaoy/yaxizhao.pdf
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Hashimoto, Kouji, Takehiko Kinoshita, and Mitsuhiro T. Nakao. "Numerical Verification of Solutions for Nonlinear Parabolic Problems." Numerical Functional Analysis and Optimization 41, no. 12 (June 12, 2020): 1495–514. http://dx.doi.org/10.1080/01630563.2020.1777159.

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Cho, Chien-Hong, and Ying-Jung Lu. "On the numerical solutions for a parabolic system with blow-up." AIMS Mathematics 6, no. 11 (2021): 11749–77. http://dx.doi.org/10.3934/math.2021683.

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<abstract><p>We study the finite difference approximation for axisymmetric solutions of a parabolic system with blow-up. A scheme with adaptive temporal increments is commonly used to compute an approximate blow-up time. There are, however, some limitations to reproduce the blow-up behaviors for such schemes. We thus use an algorithm, in which uniform temporal grids are used, for the computation of the blow-up time and blow-up behaviors. In addition to the convergence of the numerical blow-up time, we also study various blow-up behaviors numerically, including the blow-up set, blow-up rate and blow-up in $ L^\sigma $-norm. Moreover, the relation between blow-up of the exact solution and that of the numerical solution is also analyzed and discussed.</p></abstract>
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Shidfar, A., and Z. Darooghehgimofrad. "Numerical solution of two backward parabolic problems using method of fundamental solutions." Inverse Problems in Science and Engineering 25, no. 2 (January 30, 2016): 155–68. http://dx.doi.org/10.1080/17415977.2016.1138947.

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Qi-guang, Wu, and Li Ji-chun. "Numerical solutions for singularly perturbed semi-linear parabolic equation." Applied Mathematics and Mechanics 14, no. 9 (September 1993): 793–801. http://dx.doi.org/10.1007/bf02457474.

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Thapa, Dhak Bahadur, and Kedar Nath Uprety. "Analytic and Numerical Solutions of Couette Flow Problem: A Comparative Study." Journal of the Institute of Engineering 12, no. 1 (March 6, 2017): 105–13. http://dx.doi.org/10.3126/jie.v12i1.16731.

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In this work, an incompressible viscous Couette flow is derived by simplifying the Navier-Stokes equations and the resulting one dimensional linear parabolic partial differential equation is solved numerically employing a second order finit difference Crank-Nicolson scheme. The numerical solution and the exact solution are presented graphically.Journal of the Institute of Engineering, 2016, 12(1): 105-113
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Prakash, Amit, and Manoj Kumar. "Numerical solution of two dimensional time fractional-order biological population model." Open Physics 14, no. 1 (January 1, 2016): 177–86. http://dx.doi.org/10.1515/phys-2016-0021.

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AbstractIn this work, we provide an approximate solution of a parabolic fractional degenerate problem emerging in a spatial diffusion of biological population model using a fractional variational iteration method (FVIM). Four test illustrations are used to show the proficiency and accuracy of the projected scheme. Comparisons between exact solutions and numerical solutions are presented for different values of fractional orderα.
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Dissertations / Theses on the topic "Parabolic Numerical solutions"

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Zhao, Yaxi. "Numerical solutions of nonlinear parabolic problems using combined-block iterative methods /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/zhaoy/yaxizhao.pdf.

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Agueh, Martial Marie-Paul. "Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/29180.

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Ulusoy, Suleyman. "The Mathematical Theory of Thin Film Evolution." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/16213.

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We try to explain the mathematical theory of thin liquid film evolution. We start with introducing physical processes in which thin film evolution plays an important role. Derivation of the classical thin film equation and existing mathematical theory in the literature are also introduced. To explain the thin film evolution we derive a new family of degenerate parabolic equations. We prove results on existence, uniqueness, long time behavior, regularity and support properties of solutions for this equation. At the end of the thesis we consider the classical thin film Cauchy problem on the whole real line for which we use asymptotic equipartition to show H^1(R) convergence of solutions to the unique self-similar solution.
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Munyakazi, Justin Bazimaziki. "Higher Order Numerical Methods for Singular Perturbation Problems." Thesis, Online Access, 2009. http://etd.uwc.ac.za/usrfiles/modules/etd/docs/etd_gen8Srv25Nme4_6335_1277251056.pdf.

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Ranjbar, Zohreh. "Numerical Solution of Ill-posed Cauchy Problems for Parabolic Equations." Doctoral thesis, Linköpings universitet, Beräkningsvetenskap, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-54300.

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Ill-posed mathematical problem occur in many interesting scientific and engineering applications. The solution of such a problem, if it exists, may not depend continuously on the observed data. For computing a stable approximate solution it is necessary to apply a regularization method. The purpose of this thesis is to investigate regularization approaches and develop numerical methods for solving certain ill-posed problems for parabolic partial differential equations. In thermal engineering applications one wants to determine the surface temperature of a body when the surface itself is inaccessible to measurements. This problem can be modelled by a sideways heat equation. The mathematical and numerical properties of the sideways heat equation with constant convection and diffusion coefficients is first studied. The problem is reformulated as a Volterra integral equation of the first kind with smooth kernel. The influence of the coefficients on the degree of ill-posedness are also studied. The rate of decay of the singular values of the Volterra integral operator determines the degree of ill-posedness. It is shown that the sign of the coefficient in the convection term influences the rate of decay of the singular values. Further a sideways heat equation in cylindrical geometry is studied. The equation is a mathematical model of the temperature changes inside a thermocouple, which is used to approximate the gas temperature in a combustion chamber. The heat transfer coefficient at the surface of thermocouple is also unknown. This coefficient is approximated via a calibration experiment. Then the gas temperature in the combustion chamber is computed using the convection boundary condition. In both steps the surface temperature and heat flux are approximated using Tikhonov regularization and the method of lines. Many existing methods for solving sideways parabolic equations are inadequate for solving multi-dimensional problems with variable coefficients. A new iterative regularization technique for solving a two-dimensional sideways parabolic equation with variable coefficients is proposed. A preconditioned Generalized Minimum Residuals Method (GMRS) is used to regularize the problem. The preconditioner is based on a semi-analytic solution formula for the corresponding problem with constant coefficients. Regularization is used in the preconditioner as well as truncating the GMRES algorithm. The computed examples indicate that the proposed PGMRES method is well suited for this problem. In this thesis also a numerical method is presented for the solution of a Cauchy problem for a parabolic equation in multi-dimensional space, where the domain is cylindrical in one spatial direction. The formal solution is written as a hyperbolic cosine function in terms of a parabolic unbounded operator. The ill-posedness is dealt with by truncating the large eigenvalues of the operator. The approximate solution is computed by projecting onto a smaller subspace generated by the Arnoldi algorithm applied on the inverse of the operator. A well-posed parabolic problem is solved in each iteration step. Further the hyperbolic cosine is evaluated explicitly only for a small triangular matrix. Numerical examples are given to illustrate the performance of the method.
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Lawson, Jane. "Towards error control for the numerical solution of parabolic equations." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329947.

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Jürgens, Markus. "A semigroup approach to the numerical solution of parabolic differential equations." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=976761580.

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Kadhum, Nashat Ibrahim. "The spline approach to the numerical solution of parabolic partial differential equations." Thesis, Loughborough University, 1988. https://dspace.lboro.ac.uk/2134/6725.

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This thesis is concerned with the Numerical Solution of Partial Differential Equations. Initially some definitions and mathematical background are given, accompanied by the basic theories of solving linear systems and other related topics. Also, an introduction to splines, particularly cubic splines and their identities are presented. The methods used to solve parabolic partial differential equations are surveyed and classified into explicit or implicit (direct and iterative) methods. We concentrate on the Alternating Direction Implicit (ADI), the Group Explicit (GE) and the Crank-Nicolson (C-N) methods. A new method, the Splines Group Explicit Iterative Method is derived, and a theoretical analysis is given. An optimum single parameter is found for a special case. Two criteria for the acceleration parameters are considered; they are the Peaceman-Rachford and the Wachspress criteria. The method is tested for different numbers of both parameters. The method is also tested using single parameters, i. e. when used as a direct method. The numerical results and the computational complexity analysis are compared with other methods, and are shown to be competitive. The method is shown to have good stability property and achieves high accuracy in the numerical results. Another direct explicit method is developed from cubic splines; the splines Group Explicit Method which includes a parameter that can be chosen to give optimum results. Some analysis and the computational complexity of the method is given, with some numerical results shown to confirm the efficiency and compatibility of the method. Extensions to two dimensional parabolic problems are given in a further chapter. In this thesis the Dirichlet, the Neumann and the periodic boundary conditions for linear parabolic partial differential equations are considered. The thesis concludes with some conclusions and suggestions for further work.
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Bozkaya, Nuray. "Application Of The Boundary Element Method To Parabolic Type Equations." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12612074/index.pdf.

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In this thesis, the two-dimensional initial and boundary value problems governed by unsteady partial differential equations are solved by making use of boundary element techniques. The boundary element method (BEM) with time-dependent fundamental solution is presented as an efficient procedure for the solution of diffusion, wave and convection-diffusion equations. It interpenetrates the equations in such a way that the boundary solution is advanced to all time levels, simultaneously. The solution at a required interior point can then be obtained by using the computed boundary solution. Then, the coupled system of nonlinear reaction-diffusion equations and the magnetohydrodynamic (MHD) flow equations in a duct are solved by using the time-domain BEM. The numerical approach is based on the iteration between the equations of the system. The advantage of time-domain BEM are still made use of utilizing large time increments. Mainly, MHD flow equations in a duct having variable wall conductivities are solved successfully for large values of Hartmann number. Variable conductivity on the walls produces coupled boundary conditions which causes difficulties in numerical treatment of the problem by the usual BEM. Thus, a new time-domain BEM approach is derived in order to solve these equations as a whole despite the coupled boundary conditions, which is one of the main contributions of this thesis. Further, the full MHD equations in stream function-vorticity-magnetic induction-current density form are solved. The dual reciprocity boundary element method (DRBEM), producing only boundary integrals, is used due to the nonlinear convection terms in the equations. In addition, the missing boundary conditions for vorticity and current density are derived with the help of coordinate functions in DRBEM. The resulting ordinary differential equations are discretized in time by using unconditionally stable Gear'
s scheme so that large time increments can be used. The Navier-Stokes equations are solved in a square cavity up to Reynolds number 2000. Then, the solution of full MHD flow in a lid-driven cavity and a backward facing step is obtained for different values of Reynolds, magnetic Reynolds and Hartmann numbers. The solution procedure is quite efficient to capture the well known characteristics of MHD flow.
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Song, Yongcun. "An ADMM approach to the numerical solution of state constrained optimal control problems for systems modeled by linear parabolic equations." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/551.

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We address in this thesis the numerical solution of state constrained optimal control problems for systems modeled by linear parabolic equations. For the unconstrained or control-constrained optimal control problem, the first order optimality condition can be obtained in a general way and the associated Lagrange multiplier has low regularity, such as in the L²(Ω). However, for state-constrained optimal control problems, additional assumptions are required in general to guarantee the existence and regularity of Lagrange multipliers. The resulting optimality system leads to difficulties for both the numerical solution and the theoretical analysis. The approach discussed here combines the alternating direction of multipliers (ADMM) with a conjugate gradient (CG) algorithm, both operating in well-chosen Hilbert spaces. The ADMM approach allows the decoupling of the state constraints and the parabolic equation, in which we need solve an unconstrained parabolic optimal control problem and a projection onto the admissible set in each iteration. It has been shown that the CG method applied to the unconstrained optimal control problem modeled by linear parabolic equation is very efficient in the literature. To tackle the issue about the associated Lagrange multiplier, we prove the convergence of our proposed algorithm without assuming the existence and regularity of Lagrange multipliers. Furthermore, a worst case O(1/k) convergence rate in the ergodic sense is established. For numerical purposes, we employ the finite difference method combined with finite element method to implement the time-space discretization. After full discretization, the numerical results we obtain validate the methodology discussed in this thesis.
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Books on the topic "Parabolic Numerical solutions"

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Numerical solution of elliptic and parabolic partial differential equations. Cambridge: Cambridge University Press, 2012.

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Lang, Jens. Adaptive multilevel solution of nonlinear parabolic PDE systems: Theory, algorithm, and applications. Berlin: Springer, 2001.

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Vandewalle, Stefan. Parallel multigrid waveform relaxation for parabolic problems. Stuttgart: Teubner, 1993.

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Levy, M. Parabolic equation methods for electromagnetic wave propagation. London: Institution of Electrical Engineers, 2000.

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Galerkin finite element methods for parabolic problems. Berlin: Springer, 1997.

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I, Koshelev A. Regularity problem for quasilinear elliptic and parabolic systems. Berlin: Springer, 1995.

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Stability, instability, and direct integrals. Boca Raton: Chapman & Hall/CRC, 1999.

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Reshenie nekotorykh zadach dli͡a︡ parabolicheskikh uravneniĭ metodom posledovatelʹnykh priblizheniĭ. Ufa: BNT͡S︡ UrO AN SSSR, 1989.

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Daners, D. Abstract evolution equations, periodic problems and applications. Essex, England: Longman Scientific & Technical, 1992.

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Koroński, Jan. The limit problems for linear and nonlinear polyparabolic equations and asymptotic behaviour of solutions of parabolic systems. Kraków: Politechnika Krakowska im. Tadeusza Kościuszki, 2001.

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Book chapters on the topic "Parabolic Numerical solutions"

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Gheorghiu, Călin-Ioan. "Spectral Collocation Solutions to a Class of Pseudo-parabolic Equations." In Numerical Methods and Applications, 179–86. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10692-8_20.

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Lu, Xin. "Numerical Solutions of Coupled Parabolic Systems with Time Delays." In Differential Equations and Nonlinear Mechanics, 201–11. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4613-0277-3_15.

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Faragó, István, Róbert Horváth, and Sergey Korotov. "Discrete Maximum Principle for Galerkin Finite Element Solutions to Parabolic Problems on Rectangular Meshes." In Numerical Mathematics and Advanced Applications, 298–307. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18775-9_27.

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Chow, Pao-Liu, and Jing-Lin Jiang. "Almost Sure Convergence of Some Approximate Solutions for Random Parabolic Equations." In International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, 45–54. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-6413-8_3.

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Marcati, Pierangelo. "Approximate Solutions to Conservation Laws Via Convective Parabolic Equations : Analytical and Numerical Results." In Dynamics of Infinite Dimensional Systems, 169–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-86458-2_19.

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Kirsch, W., and L. A. Pastur. "Large Time Behaviour of Moments of Fundamental Solutions of the Random Parabolic Equation." In International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, 127–32. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-6413-8_9.

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Belopolskaya, Yana, and Anastasija Stepanova. "Probabilistic Algorithms for Numerical Construction of Classical Solutions to the Cauchy Problem for Nonlinear Parabolic Systems." In Analytical and Computational Methods in Probability Theory, 421–34. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71504-9_35.

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Fuhrmann, Jürgen. "On Numerical Solution Methods for Nonlinear Parabolic Problems." In Notes on Numerical Fluid Mechanics (NNFM), 170–80. Wiesbaden: Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-322-89565-3_15.

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Thomée, Vidar. "On the Numerical Solution of Integro-Differential Equations of Parabolic Type." In Numerical Mathematics Singapore 1988, 477–93. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-6303-2_39.

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Belbas, S. A. "Numerical solution of certain nonlinear parabolic partial differential equations." In Lecture Notes in Mathematics, 5–14. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0077411.

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Conference papers on the topic "Parabolic Numerical solutions"

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Ashyralyev, Allaberen, and Deniz Ağırseven. "Approximate solutions of delay parabolic equations with the Neumann condition." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756191.

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Ashyralyyeva, Maral, and Maksat Ashyraliyev. "Numerical solutions of source identification problem for hyperbolic-parabolic equations." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5049042.

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Al-Kadhi, Mohammed. "Approximation of solutions to an abstract Cauchy problem for a system of parabolic equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756586.

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Wu, Bo. "Fundamental solutions of Cauchy problem for a class of parabolic equations over p-adic field." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952036.

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Sharma, Kal Renganathan. "Effect of Relativistic Transformation Methods on the Solutions of the Damped Wave Conduction and Relaxation Equation in Semi-Infinite Medium." In ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences. ASMEDC, 2009. http://dx.doi.org/10.1115/ht2009-88523.

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The expression for transient temperature during damped wave conduction and relaxation developed by Baumeister and Hamill by the method of Laplace transforms was further integrated. A Chebyshev polynomial approximation was used for the integrand with modified Bessel composite function in space and time. Telescoping power series leads to more useful expression for transient temperature. By the method of relativistic transformation the transient temperature during damped wave conduction and relaxation was developed. There are three regimes to the solution. A regime comprising of Bessel composite function in space and time and another regime comprising of modified Bessel composite function in space and time. The temperature solution at the wave front was also developed. The solution for transient temperature from the method of relativistic transformation is compared side by side with the solution for transient temperature from the method of Chebyshev economization. Both solutions are within 12% of each other. For conditions close to the wave front the solution from the Chebyshev economization is expected to be close to the exact solution and was found to be within 2% of the solution from the method of relativistic transformation. Far from the wave front, i.e., close to the surface the numerical error from the method of Chebyshev economization is expected to be significant and verified by a specific example. The solution for transient surface heat flux from the parabolic Fourier heart conduction model and the hyperbolic damped wave conduction and relaxation models are compared with each other. For τ&gt; 1/2 the parabolic and hyperbolic solutions are within 10% of each other. The parabolic model has a “blow-up” at τ→0 and the hyperbolic model is devoid of singularities. The transient temperature from the Chebyshev economization is within an average of 25% of the error function solution for the parabolic Fourier heat conduction model. A penetration distance beyond which there is no effect of the step change in the boundary is predicted using the relativistic transformation model.
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Ashihara, Katsuhiro, and Hiromu Hashimoto. "A Rapid Method of Numerical Calculation for Oil Film Temperature in Engine Bearings." In ASME/STLE 2007 International Joint Tribology Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ijtc2007-44233.

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In the design and analysis of engine bearings for automobiles, the elastic deformation of bearing surface due to high pressure and temperature of oil film affects significantly on the bearing characteristics. Thermo-elasto-hydrodynamic lubrication analysis (TEHL) is usually used to consider such effects, but a large amount of calculation time is needed to obtain the numerical solution of oil film temperature by solving the conventional type of 3-dimensional energy equation in TEHL. This paper describes a rapid method of numerical calculation of oil film temperature in engine bearings. In this modeling, it is assumed that the temperature distribution in the oil film thickness direction takes the parabolic form. Under such an assumption, averaging the 3-dimensional energy equation over the film thickness, the 2-dimensional energy equation is newly obtained. The numerical solutions of oil film temperature based on the 2-dimensional model are compared with the solutions based on the 3-dimensional model. It is confirmed that the calculation time is remarkably reduced to obtain the oil film temperature with an allowable accuracy. Moreover, the predicted oil film temperature by the 2-dimentional model is compared with measured data, and the good agreement is seen between them.
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Hirsch, Charles, and Andrei E. Khodak. "Application of Different Turbulence Models for Duct Flow Simulation With Reduced and Full Navier-Stokes Equations." In ASME 1995 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/95-gt-145.

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An S-shaped diffusing duct flow is analysed with various turbulence models: standard high-Reynolds-number k-ε model with wall functions, a low-Reynolds-number k-ε model, and an explicit non-linear algebraic Reynolds stress closure model (ASM). In addition, computations were obtained with parabolic and partially-parabolic approximations along with solutions of the full Navier-Stokes equations. Results of the numerical simulation are compared with LDA measurements of the turbulent flow as reported by Whitelaw and Yu (1993). Detailed comparisons of mean velocity and Reynolds stress distributions are presented. It is shown that the partially-parabolic approach gives a significant improvement over parabolic approximation in predicting mean velocities and pressure distributions. However, the turbulence models used are still not able to reproduce all the observed flow features, although the ASM results appear to be slightly but consistently closer to the experimental data.
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8

Lilley, David G. "Computational Methods Using Excel/VBA for Engineering Applications." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99172.

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The focus is that Excel/VBA provides a useful platform for engineering calculations in energy engineering. It includes computational methods in the simulation and solution of engineering problems that may or may not have analytical exact mathematical solutions. Emphasis is on the methods and applications, using Excel as the interface for data input and output, tables and figures, and Visual Basic for Applications VBA as the programming language for computations. Fundamental topics of: • Linear and Nonlinear Sets of Equations; • Interpolating Polynomials; • Differentiation and Integration; • Solution of ODEs – Initial and Boundary Value Problems; • Solution of PDEs – Elliptic, Parabolic and Hyperbolic; • Graphics, including Plotting and Data Presentation, and Curve Fitting. Connections are made between each topic and a variety of engineering problems and applications. In this approach, it is emphasized how to develop and apply numerical techniques to solve engineering problems.
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9

Wang, J., S. M. Calisal, and W. Qiu. "Interactions Between Vertical Structures in Waves." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67539.

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This paper presents experimental and theoretical results obtained during the hydrodynamic study of a multi-cylinder system. The main focus of the study was to quantify hydrodynamic interactions between heaving vertical cylinders of a conceptual wave energy conversion system. Several identical circular cylinders representing platforms in an energy conversion system and a parabolic shaped wave reflector were tested in a wave flume tank. Wave heaving forces, radiation and diffraction effects were studied experimentally and numerically. The theoretical calculations were carried out for hydrodynamic coefficients, the radiation and diffraction effect analysis. Experimental results for multi-cylinders were compared with the numerical solutions by a panel-free method in the frequency domain. One main objective of the experimental tests was to calibrate the experimental set up, obtain validation data for numerical calculations. The diffraction studies showed that the hydrodynamic interactions could be constructive or destructive for heave wave forces. The positive magnification of the wave exciting force can be significant if a parabolic shaped reflector is used. It was observed that the wave force magnification and the wave energy absorption depend on incoming wavelength, and the cylinder to wavelength ratio. It has been found in the radiation tests that heave added mass and damping coefficients compare well with the calculations based on potential flow calculations.
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10

Nguyen, Kim Dan, and Rajendra K. Ray. "An Unstructured Finite-Volume Technique for Shallow-Water Flows With Wetting and Drying Fronts." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-35017.

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An unstructured finite volume numerical model is presented here for simulating shallow-water flows with wetting and drying fronts. The model is based on the Green’s theorem in combination with Chorin’s projection method. A 2nd-order upwind scheme coupled with a Least Square technique is used to handle convection terms. An Wetting and drying treatment is used in the present model to ensures the total mass conservation. To test it’s capacity and reliability, the present model is used to solve the Parabolic Bowl problem. We compare our numerical solutions with the corresponding analytical and existing standard numerical results. Excellent agreements are found in all the cases.
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