In this paper, a numerical collocation methodis developed for solving linear and nonlinear Volterra integralequations of the second kind. The method is based on theapproximation of the (exact) solution by a superposition ofsigmoidal functions and allows one to solve a large class ofintegral equations having either continuous or Lp solutions.Special computational advantages are obtained using unit stepfunctions, and analytical approximations of the solution arealso at hand. The numerical errors are discussed, and apriori as well as a posteriori estimates are derived for them.Numerical examples are given for the purpose of illustration. © 2013 Rocky Mountain Mathematics Consortium.
Solving volterra integral equations of the second kind by sigmoidal functions approximation
Costarelli D.;
2013
Abstract
In this paper, a numerical collocation methodis developed for solving linear and nonlinear Volterra integralequations of the second kind. The method is based on theapproximation of the (exact) solution by a superposition ofsigmoidal functions and allows one to solve a large class ofintegral equations having either continuous or Lp solutions.Special computational advantages are obtained using unit stepfunctions, and analytical approximations of the solution arealso at hand. The numerical errors are discussed, and apriori as well as a posteriori estimates are derived for them.Numerical examples are given for the purpose of illustration. © 2013 Rocky Mountain Mathematics Consortium.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
