Asymptotic numerical methods for singularly perturbed fourth order ordinary differential equations of convection-diffusion type (Q1855904)

Singularly perturbed boundary value problems for fourth-order ordinary differential equations are investigated. The special form of the boundary conditions allows a reduction of the problem into a system of two second-order boundary value problems. The resulting equations are then discretized with several types of finite difference schemes. An estimation of the local error with regard to the step-size and the size of the singular perturbation parameter is shown. Moreover, an extension of the suggested schemes to nonlinear problems is given. Finally, numerical computations with special test equations confirm the order of the local error.