Differential equations with piecewise approximate coefficients: Discrete and continuous estimation for initial and boundary value problems
Given a linear second order differential equation together with initial and boundary conditions which guarantee the existence of a unique solution, the authors study the effect of perturbations of the original coefficients of the differential equation on the solution of the corresponding initial or boundary value problems. As remarked in the paper such a study is interesting not only in perturbation theories but also in the numerical solution of initial and boundary value problems by means of Tau and Galerkin type methods. Since it is common in some numerical methods to replace the coefficients of the differential equation by piecewise continuous approximations defined in a suitable way, a natural question is to bound or estimate the effect of such a replacement of the solution. Here, assuming piecewise approximate coefficients, the authors derive error estimates for both the solution and its derivative of discrete and continuous initial and boundary value problems. Finally, a number of numerical examples to show the quality of the estimates are presented.
linear second order differential equation
scientific article; zbMATH DE number 148278
scientific article