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Journal articles on the topic 'Application of the partial differential equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Weerakoon, Sunethra. "Application of Sumudu transform to partial differential equations." International Journal of Mathematical Education in Science and Technology 25, no. 2 (April 1994): 277–83. http://dx.doi.org/10.1080/0020739940250214.

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2

代, 莹. "Application of Partial Differential Equations in Mathematical Models." Pure Mathematics 09, no. 06 (2019): 730–48. http://dx.doi.org/10.12677/pm.2019.96097.

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3

Stanković, B. "S-Bounded distributions, application to partial differential equations." Applicable Analysis 48, no. 1-4 (February 1993): 99–112. http://dx.doi.org/10.1080/00036819308840152.

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4

Bhalekar, Sachin, and Varsha Daftardar-Gejji. "New iterative method: Application to partial differential equations." Applied Mathematics and Computation 203, no. 2 (September 2008): 778–83. http://dx.doi.org/10.1016/j.amc.2008.05.071.

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5

Thornber, Mark, and G. L. Lamb. "Introductory Applications of Partial Differential Equations." Mathematical Gazette 83, no. 496 (March 1999): 184. http://dx.doi.org/10.2307/3618750.

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6

Morro, Angelo. "Introductory applications of partial differential equations." Meccanica 31, no. 6 (December 1996): 717–21. http://dx.doi.org/10.1007/bf00426978.

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7

Tahara, Hidetoshi. "Coupling of Two Partial Differential Equations and its Application." Publications of the Research Institute for Mathematical Sciences 43, no. 3 (2007): 535–83. http://dx.doi.org/10.2977/prims/1201012034.

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8

Fangliang, Dong. "Maximum Principle and Application of Parabolic Partial Differential Equations." IERI Procedia 3 (2012): 198–205. http://dx.doi.org/10.1016/j.ieri.2012.09.033.

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9

Manohar, R., and T. Y. Ngai. "Application of iteration functions to elliptic partial differential equations." Computers & Mathematics with Applications 16, no. 4 (1988): 279–85. http://dx.doi.org/10.1016/0898-1221(88)90144-7.

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10

Dattoli, G., B. Germano, M. R. Martinelli, and P. E. Ricci. "Monomiality and partial differential equations." Mathematical and Computer Modelling 50, no. 9-10 (November 2009): 1332–37. http://dx.doi.org/10.1016/j.mcm.2009.06.013.

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11

Kaptsov, O. V. "B-determining equations: applications to nonlinear partial differential equations." European Journal of Applied Mathematics 6, no. 3 (June 1995): 265–86. http://dx.doi.org/10.1017/s0956792500001832.

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We introduce the concept of B-determining equations of a system of partial differential equations that generalize the defining equations of the symmetry groups. We show how this concept may be applied to obtain exact solutions of partial differential equations. The exposition is reasonable self-contained, and supplemented by examples of direct physical importance, chosen from fluid mechanics.

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12

van der Walt, Jan Harm. "Solutions of Smooth Nonlinear Partial Differential Equations." Abstract and Applied Analysis 2011 (2011): 1–37. http://dx.doi.org/10.1155/2011/658936.

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The method of order completion provides a general and type-independent theory for the existence and basic regularity of the solutions of large classes of systems of nonlinear partial differential equations (PDEs). Recently, the application of convergence spaces to this theory resulted in a significant improvement upon the regularity of the solutions and provided new insight into the structure of solutions. In this paper, we show how this method may be adapted so as to allow for the infinite differentiability of generalized functions. Moreover, it is shown that a large class of smooth nonlinear PDEs admit generalized solutions in the space constructed here. As an indication of how the general theory can be applied to particular nonlinear equations, we construct generalized solutions of the parametrically driven, damped nonlinear Schrödinger equation in one spatial dimension.

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13

Benhammouda, Brahim, Hector Vazquez-Leal, and Arturo Sarmiento-Reyes. "Modified Reduced Differential Transform Method for Partial Differential-Algebraic Equations." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/279481.

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This work presents the application of the reduced differential transform method (RDTM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-two and index-three are solved to show that RDTM can provide analytical solutions for PDAEs in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful technique to find exact solutions. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend on a perturbation parameter.

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14

He, Ya Li, Ya Mian Peng, and Li Chao Feng. "Numerical Method Research of Partial Differential Equations Inverse Problem." Applied Mechanics and Materials 50-51 (February 2011): 455–58. http://dx.doi.org/10.4028/www.scientific.net/amm.50-51.455.

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It is feasible for the inverse problem of research in the very vital significance between in practical application. Genetic algorithm is applied in many aspects, but we are more concerned with the application in mathematics. From the start of genetic algorithm, the collection to search for comprehensive coverage of preferred. Due to genetic algorithm is used to search the information, and does not need such problems with the problem is directly related to the derivative of the information. Finally, the results of numerical simulation show that the GA method has high accuracy and quick convergent speed. And it is easy to program and calculate. It is worth of practical application.

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15

Papachristou, C. J., and B. Kent Harrison. "Isogroups of differential ideals of vector-valued differential forms: Application to partial differential equations." Acta Applicandae Mathematicae 11, no. 2 (February 1988): 155–75. http://dx.doi.org/10.1007/bf00047285.

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16

Abdel-Salam, Emad A. B., and Dogan Kaya. "Application of New Triangular Functions to Nonlinear Partial Differential Equations." Zeitschrift für Naturforschung A 64, no. 1-2 (February 1, 2009): 1–7. http://dx.doi.org/10.1515/zna-2009-1-201.

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The results of some new research on a new class of triangular functions that unite the characteristics of the classical triangular functions are presented. Taking into consideration the great role played by triangular functions in geometry and physics, it is possible to expect that the new theory of the triangular functions will bring new results and interpretations in mathematics, biology, physics and cosmology. New traveling wave solutions of some nonlinear partial differential equations are obtained in a unified way. The main idea of this method is to express the solutions of these equations as a polynomial in the solution of the Riccati equation that satisfy the symmetrical triangular Fibonacci functions. We apply this method to the combined Korteweg-de Vries (KdV) and modified KdV (mKdV) equations, the generalized Kawahara equation, Ito’s 5th-order mKdV equation and Ito’s 7th-order mKdV equation.

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17

He, Mengxing, Zhuoling Ou, and Anping Liu. "Comparison method of partial functional differential equations and its application." Applied Mathematics and Computation 125, no. 2-3 (January 2002): 271–86. http://dx.doi.org/10.1016/s0096-3003(00)00129-6.

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18

Khutortsev, V. V. "Application of stochastic equivalence for solving parabolic partial differential equations." Computational Mathematics and Mathematical Physics 46, no. 3 (March 2006): 402–12. http://dx.doi.org/10.1134/s0965542506030079.

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19

Sánchez-Bernabe, Francisco J., and J. Salcedo. "Application of quadratures and operator splitting to partial differential equations." Journal of Physics: Conference Series 410 (February 8, 2013): 012060. http://dx.doi.org/10.1088/1742-6596/410/1/012060.

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20

Jafari, H., M. Saeidy, and M. Zabihi. "Application of homotopy perturbation method to multidimensional partial differential equations." International Journal of Computer Mathematics 87, no. 11 (September 2010): 2444–49. http://dx.doi.org/10.1080/00207160802649965.

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21

Boukary, Beyi, Joseph Bonazebi-Yindoula, Justin Loufouilou Mouyedo, Longin Some, and Gabriel Bissanga. "Application of the SBA method for solving partial differential equations." Nonlinear Analysis and Differential Equations 6, no. 3 (2018): 91–103. http://dx.doi.org/10.12988/nade.2018.866.

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22

Cirulis, T., and O. Lietuvietis. "APPLICATION OF DM METHODS FOR PROBLEMS WITH PARTIAL DIFFERENTIAL EQUATIONS." Mathematical Modelling and Analysis 7, no. 2 (December 15, 2002): 191–200. http://dx.doi.org/10.3846/13926292.2002.9637191.

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Two variants of applications of the Degenerate Matrix Method for solving problems with PDB are considered. Solutions of the simple testing problem and of one more complicated nonlinear problem with PDB of the fifth order are presented as examples.

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23

Eslami, M., B. Fathi Vajargah, M. Mirzazadeh, and A. Biswas. "Application of first integral method to fractional partial differential equations." Indian Journal of Physics 88, no. 2 (October 2, 2013): 177–84. http://dx.doi.org/10.1007/s12648-013-0401-6.

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24

Cveticanin, L. "Application of homotopy-perturbation to non-linear partial differential equations." Chaos, Solitons & Fractals 40, no. 1 (April 2009): 221–28. http://dx.doi.org/10.1016/j.chaos.2007.07.053.

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25

Gowar, Norman, R. P. Gilbert, and H. C. Howard. "Ordinary and Partial Differential Equations with Applications." Mathematical Gazette 75, no. 473 (October 1991): 388. http://dx.doi.org/10.2307/3619544.

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26

III, Samuel M. Rankin. "Semilinear Evolution Equations in Banach Spaces with Application to Parabolic Partial Differential Equations." Transactions of the American Mathematical Society 336, no. 2 (April 1993): 523. http://dx.doi.org/10.2307/2154361.

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27

Rankin, Samuel M. "Semilinear evolution equations in Banach spaces with application to parabolic partial differential equations." Transactions of the American Mathematical Society 336, no. 2 (February 1, 1993): 523–35. http://dx.doi.org/10.1090/s0002-9947-1993-1052911-5.

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28

kaur, Dr Jatinder. "A REVIEW ON NUMERICAL METHODS FOR NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS." Journal of University of Shanghai for Science and Technology 23, no. 07 (August 1, 2021): 1342–52. http://dx.doi.org/10.51201/jusst/21/07230.

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Progression in innovation and engineering presents us with numerous difficulties, comparably to conquer such engineering difficulties with the assistance of various numerical models, equations are taken. Since in the first place Mathematicians, Designers and Engineers make progress toward accuracy what’s more, exactness while addressing equations Differential equations, specifically, hold an enormous application in engineering and numerous different areas. One such sort of Differential equation is known as partial differential equation. The range of application of partial differential equations comprises of recreation, calculation age, and investigation of higher request PDE and wave equations. Adjusting diverse numerical methods prompts an assortment of answers and contrast among them, subsequently the determination of the method of addressing is one of the urgent boundaries to produce exact outcomes. Our work centres’ around the survey of various numerical methods to settle Non-linear differential equations based on exactness and effectiveness, in order to diminish the emphases. These would orchestrate rules to existing numerical methods of nonlinear partial differential equations.[1]

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29

Adomian, G. "Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations." International Journal of Mathematics and Mathematical Sciences 12, no. 1 (1989): 137–43. http://dx.doi.org/10.1155/s0161171289000190.

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The decomposition method is applied to examples of hyperbolic, parabolic, and elliptic partial differential equations without use of linearizatlon techniques. We consider first a nonlinear dissipative wave equation; second, a nonlinear equation modeling convectlon-diffusion processes; and finally, an elliptic partial differential equation.

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30

Syazana Saharizan, Nur, and Nurnadiah Zamri. "Numerical solution for a new fuzzy transform of hyperbolic goursat partial differential equation." Indonesian Journal of Electrical Engineering and Computer Science 16, no. 1 (October 1, 2019): 292. http://dx.doi.org/10.11591/ijeecs.v16.i1.pp292-298.

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<p>The main objective of this paper is to present a new numerical method with utilization of fuzzy transform in order to solve various engineering problems that represented by hyperbolic Goursat partial differentical equation (PDE). The application of differential equations are widely used for modelling physical phenomena. There are many complicated and dynamic physical problems involved in developing a differential equation with high accuracy. Some problems requires a complex and time consuming algorithms. Therefore, the application of fuzzy mathematics seems to be appropriate for solving differential equations due to the transformation of differential equations to the algebraic equation which is solvable. Furthermore, development of a numerical method for solving hyperbolic Goursat PDE is presented in this paper. The method are supported by numerical experiment and computation using MATLAB. This will provide a clear picture to the researcher to understand the utilization of fuzzy transform to the hyperbolic Goursat PDE.</p>

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31

De Meyer, Bernard. "Repeated Games and Partial Differential Equations." Mathematics of Operations Research 21, no. 1 (February 1996): 209–36. http://dx.doi.org/10.1287/moor.21.1.209.

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32

Aviles, Patricio, and James Sandefur. "Nonlinear second order equations with applications to partial differential equations." Journal of Differential Equations 58, no. 3 (July 1985): 404–27. http://dx.doi.org/10.1016/0022-0396(85)90008-7.

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33

YU, GUOSHENG, and BING LIU. "ON EXPONENTIAL STABILITY FOR STOCHASTIC DELAY PARTIAL DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 09, no. 01 (March 2009): 121–34. http://dx.doi.org/10.1142/s0219493709002579.

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This paper is concerned with the exponential stability of energy solutions to a nonlinear stochastic delay partial differential equations with finite delay in separable Hilbert spaces. Some exponential stability criteria are obtained by constructing the Lyapunov function. As an application, one example is also given to illustrate our results.

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34

Gad-Allah, Musa R., and Tarig M. Elzaki. "Application of New Homotopy Perturbation Method for Solving Partial Differential Equations." Journal of Computational and Theoretical Nanoscience 15, no. 2 (February 1, 2018): 500–508. http://dx.doi.org/10.1166/jctn.2018.6725.

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In this paper, a novel technique, that is to read, the New Homotopy Perturbation Method (NHPM) is utilized for solving a linear and non-linear differential equations and integral equations. The two most important steps in the application of the new homotopy perturbation method are to invent a suitable homotopy equation and to choose a suitable initial conditions. Comparing between the effects of the method (NHPM), is given exact solution, and the method (HPM), is given approximate solution, in this paper, we make some instances are provided to prove the ability of the method (NHPM). Show that the method (NHPM) is valid and effective, easy and accurate in solving linear and nonlinear differential equations, compared with the Homotopy Perturbation Method (HPM).

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35

Chaolu, Temuer, and Sudao Bilige. "Applications of Differential Form Wu’s Method to Determine Symmetries of (Partial) Differential Equations." Symmetry 10, no. 9 (September 3, 2018): 378. http://dx.doi.org/10.3390/sym10090378.

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In this paper, we present an application of Wu’s method (differential characteristic set (dchar-set) algorithm) for computing the symmetry of (partial) differential equations (PDEs) that provides a direct and systematic procedure to obtain the classical and nonclassical symmetry of the differential equations. The fundamental theory and subalgorithms used in the proposed algorithm consist of a different version of the Lie criterion for the classical symmetry of PDEs and the zero decomposition algorithm of a differential polynomial (d-pol) system (DPS). The version of the Lie criterion yields determining equations (DTEs) of symmetries of differential equations, even those including a nonsolvable equation. The decomposition algorithm is used to solve the DTEs by decomposing the zero set of the DPS associated with the DTEs into a union of a series of zero sets of dchar-sets of the system, which leads to simplification of the computations.

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36

Ferraioli, D. Catalano, G. Manno, and F. Pugliese. "Generalised symmetries of partial differential equations via complex transformations." Bulletin of the Australian Mathematical Society 76, no. 2 (October 2007): 243–62. http://dx.doi.org/10.1017/s0004972700039630.

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We consider two systems of real analytic partial differential equations, related by a holomorphic contact map H. We study how the generalised symmetries of the first equation are mapped into those of the second one, and determine under which conditions on H such a map is invertible. As an application of these results, an example of physical interest is discussed.

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37

Dal, Fadime. "Application of Variational Iteration Method to Fractional Hyperbolic Partial Differential Equations." Mathematical Problems in Engineering 2009 (2009): 1–10. http://dx.doi.org/10.1155/2009/824385.

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The solution of the fractional hyperbolic partial differential equation is obtained by means of the variational iteration method. Our numerical results are compared with those obtained by the modified Gauss elimination method. Our results reveal that the technique introduced here is very effective, convenient, and quite accurate to one-dimensional fractional hyperbolic partial differential equations. Application of variational iteration technique to this problem has shown the rapid convergence of the sequence constructed by this method to the exact solution.

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38

Guillot, Jules, Guillaume Koenig, Kadi Minbashian, Emmanuel Frénod, Héléne Flourent, and Julien Brajard. "Partial differential equations for oceanic artificial intelligence." ESAIM: Proceedings and Surveys 70 (2021): 137–46. http://dx.doi.org/10.1051/proc/202107009.

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The Sea Surface Temperature (SST) plays a significant role in analyzing and assessing the dynamics of weather and also biological systems. It has various applications such as weather forecasting or planning of coastal activities. On the one hand, standard physical methods for forecasting SST use coupled ocean- atmosphere prediction systems, based on the Navier-Stokes equations. These models rely on multiple physical hypotheses and do not optimally exploit the information available in the data. On the other hand, despite the availability of large amounts of data, direct applications of machine learning methods do not always lead to competitive state of the art results. Another approach is to combine these two methods: this is data-model coupling. The aim of this paper is to use a model in another domain. This model is based on a data-model coupling approach to simulate and predict SST. We first introduce the original model. Then, the modified model is described, to finish with some numerical results.

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39

Bekar, Ali C., and Erdogan Madenci. "Peridynamics enabled learning partial differential equations." Journal of Computational Physics 434 (June 2021): 110193. http://dx.doi.org/10.1016/j.jcp.2021.110193.

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40

Messenger, Daniel A., and David M. Bortz. "Weak SINDy for partial differential equations." Journal of Computational Physics 443 (October 2021): 110525. http://dx.doi.org/10.1016/j.jcp.2021.110525.

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41

Zimmerman, W. R. "Application of circuit analysis programs to systems of partial differential equations." Numerical Methods for Partial Differential Equations 13, no. 6 (November 1997): 601–15. http://dx.doi.org/10.1002/(sici)1098-2426(199711)13:6<601::aid-num2>3.0.co;2-v.

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42

Galperin, Efim A., Zhongxiong Pan, and Quan Zheng. "Application of global optimization to implicit solution of partial differential equations." Computers & Mathematics with Applications 25, no. 10-11 (May 1993): 119–24. http://dx.doi.org/10.1016/0898-1221(93)90287-6.

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43

Rokhlin, Vladimir. "Application of volume integrals to the solution of partial differential equations." Computers & Mathematics with Applications 11, no. 7-8 (July 1985): 667–79. http://dx.doi.org/10.1016/0898-1221(85)90163-4.

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44

Mansour, Eman A., Sadiq A. Mehdi, and Emad A. Kuffi. "Application of New Transform “Complex SEE Transform” to Partial Differential Equations." Journal of Physics: Conference Series 1999, no. 1 (September 1, 2021): 012155. http://dx.doi.org/10.1088/1742-6596/1999/1/012155.

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45

Qu, Changzheng. "Reductions and exact solutions of some nonlinear partial differential equations under four types of generalized conditional symmetries." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 41, no. 1 (July 1999): 1–40. http://dx.doi.org/10.1017/s0334270000011012.

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AbstractThe generalized conditional symmetry method is applied to study the reduction to finite-dimensional dynamical systems and construction of exact solutions for certain types of nonlinear partial differential equations which have many physically significant applications in physics and related sciences. The exact solutions of the resulting equations are derived via the compatibility of the generalized conditional symmetries and the considered equations, which reduces to solving some systems of ordinary differential equations. For some unsolvable systems of ordinary differential equations, the dynamical behavior and qualitative properties are also considered. To illustrate that the approach has wide application, the exact solutions of a number of nonlinear partial differential equations are also given. The method used in this paper also provides a symmetry group interpretation to some known results in the literature which cannot be obtained by the nonclassical symmetry method due to Bluman and Cole.

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46

Tan, Nguyen Xuan. "Bifurcation from Characteristic Values for Equations Involving Fredholm Mappings with Applications to Partial Differential Equations. II Application." Mathematische Nachrichten 139, no. 1 (1988): 7–25. http://dx.doi.org/10.1002/mana.19881390102.

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47

Ibis, Birol. "Application Of Reduced Differential Transformation Method For Solving Fourth-order Parabolic Partial Differential Equations." Journal of Mathematics and Computer Science 12, no. 02 (September 23, 2014): 124–31. http://dx.doi.org/10.22436/jmcs.012.02.04.

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48

Saeed, Umer, Mujeeb ur Rehman, and Qamar Din. "Differential quadrature method for nonlinear fractional partial differential equations." Engineering Computations 35, no. 6 (August 6, 2018): 2349–66. http://dx.doi.org/10.1108/ec-04-2018-0179.

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Purpose The purpose of this paper is to propose a method for solving nonlinear fractional partial differential equations on the semi-infinite domain and to get better and more accurate results. Design/methodology/approach The authors proposed a method by using the Chebyshev wavelets in conjunction with differential quadrature technique. The operational matrices for the method are derived, constructed and used for the solution of nonlinear fractional partial differential equations. Findings The operational matrices contain many zero entries, which lead to the high efficiency of the method and reasonable accuracy is achieved even with less number of grid points. The results are in good agreement with exact solutions and more accurate as compared to Haar wavelet method. Originality/value Many engineers can use the presented method for solving their nonlinear fractional models.

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49

Dziuk, Gerhard, Charles Elliott, Gerhard Huisken, and Ralf Kornhuber. "Geometric Partial Differential Equations: Theory, Numerics and Applications." Oberwolfach Reports 8, no. 4 (2011): 3077–144. http://dx.doi.org/10.4171/owr/2011/54.

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50

Mohamad-Jawad, Anwar Ja’afar, Marko D. Petković, and Anjan Biswas. "Applications of He’s principles to partial differential equations." Applied Mathematics and Computation 217, no. 16 (April 2011): 7039–47. http://dx.doi.org/10.1016/j.amc.2011.02.013.

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