Numerical solution of nonlinear volterra integral equations with nonincreasing kernel and an application

Employing the quasilinearization technique to solve the nonlinear Volterra integral equations when the kernel of equation is nonincreasing with respect to the unknown function, yields two coupled sequences of linear Volterra integral equations where the solutions of these two sequences converge monotonically to the solution of nonlinear equation. We use collocation method and solve these coupled linear equations numerically, and obtain two sequences of successive approximations convergent to the solution of nonlinear equation. Error analysis is performed and an application to a boundary-layer theory problem and examples illustrating the results are presented.