Some Aspects of the Solution of Non-linear Differential Equations

Abstract

Nonlinear differential equations can be solved by a variety of methods. One such technique is to transform the differential equations into a set of algebraic equations. The thesis describes the methods available at present for solving large systems of algebraic equations. The methods described are found to be not to be entirely satisfactory and therefore a new technique for solving algebraic equations is presented. The technique is specifically developed for solving large systems of equations whilst simplifying the computation and minimizing the storage requirements, Next, a study has been made to provide a suitable standard of comparisons between the various methods. Finally, an industrial problem is solved using the new technique. Comparisons show that the above technique provides an adequate solution at reduced computational effort