An Efficient Numerical Approach to Solve Fractional Coupled Boussinesq Equations

Abstract

In this study, we compute and analyze the numerical solution of fractional coupled Boussinesq equations using fractional-order Laguerre operational matrices of differentiation. The fractional derivative is taken into Caputo's sense. In the first step, we derived a pseudo-operational matrix of differentiation for integer and fractional order. We approximated each term of the fractional coupled Boussinesq equations in terms of the pseudo-operational matrix. Hence, we get the fractional coupled Boussinesq equation in matrix representation. A system of algebraic equations is obtained by collocating this system at Newton–Cotes nodal points, which can be solved easily with Newton's iterative method. The function approximation error estimate has also been discussed. The proposed approach is simple, accurate and produces numerical results with high accuracy, which is evidenced by the given numerical results.