On the reliable balancing collocation technique for a class of linear two-dimensional Fredholm–Volterra integral equations

Abstract

In this work, a reliable and efficient numerical technique viz. the balancing collocation technique (BCT) has been introduced and employed to solve the linear two-dimensional Fredholm–Volterra integral (F–VI) equations. The technique reduces the solution of these integral equations to the solution of a linear system of algebraic equations. Furthermore, the convergence and error analysis have been presented for the proposed methodology. Apart from that, the existence and uniqueness of the solutions obtained have been discussed. In addition, certain numerical examples have been discussed to demonstrate the accuracy and effectiveness of the proposed technique. Furthermore, certain comparative graphs for the BCT solutions and exact solutions have been depicted to illustrate the efficiency of the technique.

Keywords

• Balancing polynomials
• Collocation scheme
• Fredholm–Volterra integral equations
• Polynomial approximation