Differential Equations Via Approximation Methods

Abstract

When the known algebraic methods for solving differential equations and systems of differential equations offer no solution, we usually resort to methods of approximation. The approximation methods can involve both symbolic and numerical work. The symbolic approach yields approximate algebraic solutions, and its most representative technique is the Taylor series method. The numerical approach yields a solution in the form of a finite set of solution points, to which a curve can be fitted by various algebraic methods (interpolation, regression,…). This curve will be an approximate solution of the differential equation. Among the most common numerical methods is the Runge–Kutta method.