Add to ORKGA new class of multistep methods for stiff ordinary differential equations is presented. The method is based in the application of estimation functions for the derivatives and the state variables, allowing the transformation of the original system in a purely algebraic system using the solutions of previous steps. From this point of view these methods adopt a semi-implicit scheme. The novelty introduced is an adaptive formula for the estimation function coefficients, deduced from a combined analysis of stability and convergence order. That is, the estimation function coefficients are recomputed at each time step. The convergence order of the resulting scheme is better than the equivalent linear multistep methods, while preserving the proper...
AbstractTwo efficient third-and fourth-order processes for solving the initial value problem for ord...
PhD ThesisIn this thesis several topics in the numerical solution of the initial value problem in f...
AbstractA substantial increase in efficiency is achieved by the numerical integration methods which ...
AbstractThe α-type multistep methods have the form of Yn+kαnYn+k-1+(αn-1)Yn+k-2=hn+kΣi=0kβi,nfn+1 wh...
Backward differentiation methods are used extensively for integration of stiff systems of ordinary d...
AbstractA model is presented for stability for an extension of linear multistep methods for stiff or...
In this paper, we present a class of hybrid multistep methods for the numerical solution of first-...
AbstractThe aim of this paper is to select from the large family of possible general linear methods,...
AbstractA multistep method with matricial coefficients is developed. It can be used to solve stiff i...
summary:The paper is concerned with the numerical solution of ordinary differential equations by a n...
summary:The paper is concerned with the numerical solution of ordinary differential equations by a n...
We have recently proposed a variational framework for the approximation of systems of differential e...
AbstractA sixth-order A-stable explicit one-step method for stiff ordinary differential equations is...
AbstractSome k-step kth order explicit nonlinear multistep methods (NMM) are proposed for both stiff...
AbstractA family of nonlinear multistep (NLMS) methods is formulated to be A-stable in the sense of ...
AbstractTwo efficient third-and fourth-order processes for solving the initial value problem for ord...
PhD ThesisIn this thesis several topics in the numerical solution of the initial value problem in f...
AbstractA substantial increase in efficiency is achieved by the numerical integration methods which ...
AbstractThe α-type multistep methods have the form of Yn+kαnYn+k-1+(αn-1)Yn+k-2=hn+kΣi=0kβi,nfn+1 wh...
Backward differentiation methods are used extensively for integration of stiff systems of ordinary d...
AbstractA model is presented for stability for an extension of linear multistep methods for stiff or...
In this paper, we present a class of hybrid multistep methods for the numerical solution of first-...
AbstractThe aim of this paper is to select from the large family of possible general linear methods,...
AbstractA multistep method with matricial coefficients is developed. It can be used to solve stiff i...
summary:The paper is concerned with the numerical solution of ordinary differential equations by a n...
summary:The paper is concerned with the numerical solution of ordinary differential equations by a n...
We have recently proposed a variational framework for the approximation of systems of differential e...
AbstractA sixth-order A-stable explicit one-step method for stiff ordinary differential equations is...
AbstractSome k-step kth order explicit nonlinear multistep methods (NMM) are proposed for both stiff...
AbstractA family of nonlinear multistep (NLMS) methods is formulated to be A-stable in the sense of ...
AbstractTwo efficient third-and fourth-order processes for solving the initial value problem for ord...
PhD ThesisIn this thesis several topics in the numerical solution of the initial value problem in f...
AbstractA substantial increase in efficiency is achieved by the numerical integration methods which ...