A NEW ITERATIVE SCHEME FOR THE SOLUTION OF TENTH ORDER BOUNDARY VALUE PROBLEMS USING FIRST-KIND CHEBYCHEV POLYNOMIALS
Ebimene James Mamadu, Ignatius Nkonyeasua Njoseh.
Abstract
In this paper, a new iterative scheme for the solution of tenth order boundary value problems is implemented using first-kind Chebychev polynomials as trial functions. The method involves transforming the tenth order boundary value problems into a system of ordinary differential equations (ODEs). The trial solution is introduced into the ODEs, and is evaluated at the boundaries to obtain the approximate solution. The method avoids quasi-linearization, linearization, discretization or perturbation. Also, the method is computationally simple with round-off and truncation errors avoided. Numerical results obtained with the method show that the method is highly reliable and accurate in obtaining the approximate solution of tenth order boundary value problems as compared with the results generated from the Galerkin method available in the literature. All computations are performed with maple 18 software.
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