CHEBYSHEV COMPUTATIONAL ALGORITHM FOR EIGHT ORDER BOUNDARY VALUE PROBLEMS

Document Type : Regular research papers

Authors

1 Department of Applied Sciences, Federal College of Dental Technology and Therapy, Enugu, Nigeria

2 Department of Statistics,Federal Polytechnic Ede, Osun, Nigeria

3 Department of Mathematics and Statistics, Federal University Wukari Taraba,670101 Nigeria.

4 Department of Mathematics, University Ilesa, Osun, Nigeria.

Abstract

In this research, we present a computational algorithm designed for solving eighth-order Boundary Value Problems(BVPs) using fourth-kind Chebyshev polynomials as basis functions. The method entails assuming an approximate solution employing fourth-kind shifted Chebyshev polynomials. Subsequently, this assumed solution is substituted into the relevant problem. The resulting equation is collocated at evenly spaced points within the interval, resulting in a linear system of equations with unknown Chebyshev coefficient constants. To solve this system, we employ a matrix inversion approach to determine the unknown constants, which are then substituted back into the assumed solution to obtain the desired approximate solution. To validate the effectiveness of the proposed technique, three numerical examples are selected from existing literature. The results obtained from our method are compared with those reported in the literature, demonstrating that the proposed algorithm is not only accurate but also efficient in solving BVPs. Tables and figures are employed to present and illustrate the results.

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