Exact and Approximate to Exact Methods for Solution Linear Boundary Value Problems Using Laplace Transform.

Document Type : Original Article

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Department of Basic Science, Engineering Division, International Academy for Engineering and Media Science

Abstract

 It is a new method, a mixture of numerical and exact methods, each of
which has a role to obtain the solution. It is known that the Laplace transforms
method gives a closed-form for initial value problems but in the present study, we
were able to use it with the aid of high-accurate numerical methods to solve linear
boundary value problems. The novelty of the present method that it is converted
Linear Boundary Value Problems to initial Value Problems using accurate
numerical methods and then uses Laplace transforms method to find approximate
to the exact solution. Approximate to Exact Method (AEM) is an algorithm, with a
very strong accuracy that approaches the exact solution because it is a mixture of
numerical methods of very high accuracy with a closed-form method. The
uniqueness, convergence, and stability of the new technique are verified and tested
by comparisons with a fourth-order accurate finite difference (FOFDM) solution.

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