Multivalue Almost Collocation Methods with Diagonal Coefficient Matrix

Abstract

We introduce a family of multivalue almost collocation methods with diagonal coefficient matrix for the numerical solution of ordinary differential equations. The choice of this type of coefficient matrix permits a reduction of the computational cost and a parallel implementation. Collocation gives a continuous extension of the solution which is useful for a variable step size implementation. We provide examples of A-stable methods with two and three stages and order 3.