Second-order a priori and a posteriori error estimations for integral boundary value problems of nonlinear singularly perturbed parameterized form

Abstract

In this work, we present the a priori and a posteriori error analysis of a hybrid difference scheme for integral boundary value problems of nonlinear singularly perturbed parameterized form. The discretization for the nonlinear parameterized equation constitutes a hybrid difference scheme which is based on a suitable combination of the trapezoidal scheme and the backward difference scheme. Further, we employ the composite trapezoidal scheme for the discretization of the nonlocal boundary condition. A priori error estimation is provided for the proposed hybrid scheme, which leads to second-order uniform convergence on various a priori defined meshes. Moreover, a detailed a posteriori error analysis is carried out for the present hybrid scheme which provides a proper discretization of the error equidistribution at each partition. Numerical results strongly validate the theoretical findings for nonlinear problems with integral boundary conditions.