Algebraic Method for Solving Linear Partial Differential Equations with Variable Coefficients. Part I: Basic Theory

1979 ◽  
Vol 10 (3) ◽  
pp. 586-602 ◽  
Author(s):  
Serge Vasilach
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Algebraic Method ◽  
Variable Coefficients ◽  
Basic Theory ◽  
Partial Differential ◽  
Linear Partial Differential Equations

scholarly journals Using the Differential Transform Method to Solve Non-Linear Partial Differential Equations

2020 ◽  
pp. 34-43
Author(s):  
Fadwa A. M. Madi ◽  
Fawzi Abdelwahid
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Variable Coefficients ◽  
Differential Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Linear Partial Differential Equations ◽  
Differential Transform ◽  
Non Linear

In this work, we reviewed the two-dimensional differential transform, and introduced the differential transform method (DTM). As an application, we used this technique to find approximate and exact solutions of selected non-linear partial differential equations, with constant or variable coefficients and compared our results with the exact solutions. This shows that the introduced method is very effective, simple to apply to linear and nonlinear problems and it reduces the size of computational work comparing with other methods.

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