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Abstract
This study deals with the following method for solving ordinary differential equations and solving linear and non linear differential equation A application of the matrix method to the one dimensional heat equation.
The matrix method for solving integral equations to introduced, and also application to the problem of the two dimensional sails. This study iutistratea the matrix method by examples @ compares the method with other known methods, which use Fourier series an a basis like the method of Plousbaw for linear differential equations and nonlinear differential equations, the methods of D. Allot for the heat equation and for fredholm integral equations and also the of Thwarts for the sell equation.