Fourth Order Initial Value Problems Research Articles

Direct Block Predictor-Corrector Method for the Solution of General Fourth Order Odes

This article presented the direct block predictor-corrector method for solving general higher order initial value problems of ordinary differential equation. Method of collocation and interpolation of power series approximate solution was used to derive a continuous linear multistep method. Block method was later used to generate the non overlapping solution at selected grid points. The method developed, is self starting, consistent, symmetric, zero-stable and convergent. The performance of the new block method was tested with some fourth order initial value problems and it was found to compare favorably with the existing methods.

A mixed finite element method for solving the nonstationary stokes equation

This paper deals with a mixed finite element method for approximating a fourth order initial value problem arising from the nonstationary Stokes problem. For piecewise linear shape functions error estimates are given with convergence rates similar to the elliptic case. Some numerical computations will illustrate the theoretical results.

An integral representation for eigenfunctions of linear ordinary differential operators

This paper generalizes an integral representation formula for eigenfunctions of Sturm-Liouville operators, known as the Volterra transformation operator in the theory of the inverse scattering problem, to higher-order differential operators. A specific fourth-order initial value problem is considered: Lφ = k 4φ, L = d 4 dx 4 + d dx (q d dx ) + r φ(0) = 1, φ′(0) = 0, φ″(0) = − k 2, φ‴ = 0 The solution for complex k is expressed as an inverse-Laplace-Borel transform. Jump formulae are obtained relating the representing kernel directly to the coefficients of L. The result admits obvious generalization to operators of arbitrary order.