Numerical Solution of Singular Stochasticintegral Equations of Abel’s Type Usingoperational Matrix Method

This paper proposes the orthogonal shifted Legendre collocation method to obtain an approximate solution for Abel-type singular linear stochastic integral equation. Our proposed method converts the singular linear stochastic equation to a system of algebraic equations. The shifted Legendre polynomials are used to obtain the operational matrices for such a conversion. The main advantage of the proposed method is that a sparse, tridiagonal orthogonal matrix is obtained, thus making process simple and efficient. The convergence and error analysis of the proposed method are discussed. Numerical examples prove the applicability and the efficiency of our proposed method.