Solution of different type of the partial differential equation by differential transform method and Adomian's decomposition method

Abstract In this paper, the definitions and operations of the differential transform method [J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huarjung University Press, Wuuhahn, China, 1986] and Adomian’s decomposition method which is given by George Adomian for approximate solution of linear and non-linear differential equations are expressed [G. Adomian, Convergent series solution of nonlinear equation, Comput. Appl. Math. 11 (1984) 113–117] . Different partial differential equations are solved under the view of these methods and compared with the approximate solution and analytic solution. At the end, these solutions are illustrated by tables and figures.

[1]  E. Zauderer,et al.  Partial Differential Equations of Applied Mathematics: Zauderer/Partial , 2006 .

[2]  R. Dennemeyer,et al.  Introduction to partial differential equations and boundary value problems / Rene Dennemeyer , 1969 .

[3]  Cha'o-Kuang Chen,et al.  Solving partial differential equations by two-dimensional differential transform method , 1999, Appl. Math. Comput..

[4]  Y. C. Liu,et al.  Solution of Two-Point Boundary-Value Problems Using the Differential Transformation Method , 1998 .

[5]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[6]  Ming-Jyi Jang,et al.  Analysis of the response of a strongly nonlinear damped system using a differential transformation technique , 1997 .

[7]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[8]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[9]  W. Strauss,et al.  Partial Differential Equations: An Introduction , 1992 .

[10]  Y. Cherruault,et al.  Convergence of Adomian's method applied to nonlinear equations , 1994 .

[11]  George Adomian,et al.  Modified Adomian Polynomials , 1996 .

[12]  Sherman X. Bai,et al.  Multiperiod production planning with demand and cost fluctuation , 1998 .

[13]  G. Adomian,et al.  Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations , 1990 .

[14]  L. Debnath.  Nonlinear Partial Differential Equations for Scientists and Engineers , 1997 .

[15]  George Adomian,et al.  Convergent series solution of nonlinear equations , 1984 .

[16]  G. Adomian,et al.  Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition , 1993 .

[17]  Ming-Jyi Jang,et al.  Two-dimensional differential transform for partial differential equations , 2001, Appl. Math. Comput..

[18]  Y. Cherruault,et al.  Convergence of Adomian's method applied to differential equations , 1994 .

[19]  W. Cheney,et al.  Numerical analysis: mathematics of scientific computing (2nd ed) , 1991 .