NUMERICAL SOLUTION OF INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS BY SOME CONSTRUCTED ORTHOGONAL POLYNOMIALS AS THE BASES FUNCTIONS | ||||
| Journal of Fractional Calculus and Applications | ||||
| Volume 16, Issue 1, 2025, Page 1-29 PDF (1.29 MB) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/jfca.2025.291197.1108 | ||||
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| Authors | ||||
Zachaeous Olusegun Ogunwobi1; Ayodeji Quadri Akinsanya 2; Omotayo Adebayo Taiwo  2
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| 1Mathematical Sciences, Science, Olabisi Onabanjo University | ||||
| 2Mathematics, Physical Sciences, University of Ilorin | ||||
| Abstract | ||||
| In this paper, standard collocation approximation method is used as the numerical solution of integral and integro-differential equations. Two types of orthogonal polynomials are constructed and used as bases functions. The method assumed an approximate solution using the orthogonal polynomials constructed as basis function which are then substituted into the problem considered. Then, the like terms of the unknown coefficients are collected and simplified. The resulting equation is then collocated at equally spaced interior points hence leading to algebraic linear system of equations which are then solved by Guassian elimination method to obtain the unknown constants. These are substituted back into the assumed approximate solution to get the required approximate solution. Numerical solution are given to illustrate the accuracy of the method discussed in the work. It was observed that as the degree of approximant increases, approximate solution tends to the exact solution. These are evident in the graph presented. | ||||
| Keywords | ||||
| Standard collocation method; Basis Function; Integral and Integro-differential equations and Guassian elimination | ||||
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