A higher-order hybrid finite difference method based on grid equidistribution for fourth-order singularly perturbed differential equations

The paper presents a higher-order parameter uniform numerical approximation of a fourth-order singularly perturbed boundary value problem on a non-uniform grid. The given problem is converted into a coupled system of singularly perturbed differential equations. The coupled system of equation is discretized on a non-uniform mesh using a higher-order hybrid difference scheme. The grid equidistribution principle, based on a positive monitor function, is used to formulate the grid. The properties of the discrete operator are utilized on the equidistributed grid to obtain fourth-order parameter uniform convergence. The convergence obtained is optimal in the sense that it is free from any logarithmic term. Numerical result for two model problems is presented, which agree with the theoretical estimates.