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A numerical solution of second-order linear partial differential equations by differential transform. (English) Zbl 1090.65134

The authors propose a general numerical solution of of second-order linear partial differential equations using two-dimensional differential transform. Numerical results are presented to confirm the proposed scheme.

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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References:

[1] Ayaz, F., On the two-dimensional differential transform method, Applied Mathematics and Computation, 143, 361-374 (2003) · Zbl 1023.35005
[2] Ayaz, F., Solutions of the system of differential equations by differential transform method, Applied Mathematics and Computation, 147, 547-567 (2004) · Zbl 1032.35011
[3] Biazar, J.; Ebrahimi, H., An approximation to the solution of hyperbolic equations by Adomian decomposition method and comparison with characteristics method, Applied Mathematics and Computation, 163, 633-638 (2005) · Zbl 1060.65651
[4] Chen, C. K.; Ho, S. H., Solving partial differential equations by two-dimensional differential transform method, Applied Mathematics and Computation, 106, 171-179 (1999) · Zbl 1028.35008
[5] Jang, M. J.; Chen, C. L.; Liu, Y. C., Two-dimensional differential transform for partial differential equations, Applied Mathematics and Computation, 121, 261-270 (2001) · Zbl 1024.65093
[6] Lapidus, L.; Pinder, G. F., Numerical solution of partial differential equations in science and engineering (1982), John Wiley & Sons Inc: John Wiley & Sons Inc Chichester, UK · Zbl 0584.65056
[7] Selvadurai, A. P.S., Partial differential equations in mechanics 1: fundamentals, laplace’s equation, diffusion equation, wave equation (2000), Springer-Verlag: Springer-Verlag Berlin, Heidelberg · Zbl 0967.35001
[8] Zhou, J. K., Differential transformation and its applications for electronic circuits (1986), Huazhong Science & Technology University Press: Huazhong Science & Technology University Press China, (in Chinese)
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