Convergence of monotone iterations to initial value problems of functional differential equations

Abstract

The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. We use this technique to initial value problems of functional differential equations showing that corresponding linear iterations converge to the unique solution of our problem and this convergence is superlinear

Keywords:

• Quasilinearization
• monotone iterations
• superlinear convergence

AMS:

• 34A45
• 34K99