A THREE-STEP INTERPOLATION TECHNIQUE WITH PERTURBATION TERM FOR DIRECT SOLUTION OF THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS

A Three Step Implicit Hybrid Linear Multistep Method for the Solution of Third Order Ordinary Differential Equations

A Linear Multistep Hybrid Method (LMHM) with continuous coefficients is considered and directly applied to solve third order Initial Value Problems (IVPs). The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) each of order 5 which are combined as simultaneous numerical integrators to provide a direct solution to IVPs over sub-intervals which do not overlap. The con...

INVESTIGATION OF BOUNDARY LAYERS IN A SINGULAR PERTURBATION PROBLEM INCLUDING A 4TH ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we investigate a singular perturbation problem including a fourth order O.D.E. with general linear boundary conditions. Firstly, we obtain the necessary conditions of solution of O.D.E. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.

Asymptotic Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations with a Discontinuous Source Term

A class of singularly perturbed two point Boundary Value Problems (BVPs) of reaction-diffusion type for third order Ordinary Differential Equations (ODEs) with a small positive parameter (ε) multiplying the highest derivative and a discontinuous source term is considered. The BVP is reduced to a weakly coupled system consisting of one first order ordinary differential equation with a suitable i...

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

A Six Step Block Method for Solution of Fourth Order Ordinary Differential Equations

A linear multistep method for solving first order initial value problems of ordinary differential equations is presented in this paper. The approach of collocation approximation is adopted in the derivation of the scheme and then the scheme is applied as simultaneous integrator to first order initial value problems of ordinary differential equations. This implementation strategy is more accurat...