Least Squares Technique for Solving Volterra Fractional Integro-differential Equations Based on Constructed Orthogonal Polynomials
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Akamai University, Hawaii, USA.
In this study, a new Gauss-Legendre Polynomials basis function was constructed and used for solving integro-differential difference equations using standard collocation method. An assumed approximate solution in terms of the constructed polynomial was substituted into the general class of integro-differential difference equation considered. The resulted equation was collocated at appropriate points within the interval of consideration to obtain a system of algebraic linear equations. Solving the system of equations, the unknown constant coefficients involved in the equations are obtained. The required approximate solution is obtained when the values of the constant coefficients are substituted back into the assumed approximate solution. Some numerical examples were solved to demonstrate the method.
integro-differential difference equations, Gauss-Legendre polynomials