NUMERICAL APPROXIMATION METHODS FOR SOLVING INTEGRODIFFERENTIAL EQUATIONS VIA THIRD KIND CHEBYSHEV AND LAGUERRE POLYNOMIALS
Keywords:
Collocation Method, Volterra Intrgro-differential Equations, Chebyshev Polynomial, and Laguerre Polynomial.Abstract
In this work, the collocation method via third kind Chebyshev and Laguerre polynomials as basis
functions were developed and used to solve Volterra integro-differential equations (IDEs) using
the standard collocation method. An assumed approximate solution is substituted into the given
problem, thus resulted in more unknown constants to be determined. After simplification and
collocations, resulted in linear algebraic equations which are then solved via maple 18 to obtain
unknown constants that are involved. Comparisons were made with the two trial solutions
mentioned above in terms of errors obtained. Numerical examples were given to illustrate the
performance of the method for various orders. However, the third kind Chebyshev polynomial
basis exhibits better accuracy over the Laguerre polynomials as can be seen from the tables of
errors presented.
