Continuous block implicit hybrid one-step methods for ordinary and delay differential equations

Authors:
Hongjiong Tian;Quanhong Yu;Cilai Jin
Affiliations:
Department of Mathematics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234, PR China and Division of Computational Science, E-Institute of Shanghai Universities, Scientific Computing ...;Department of Mathematics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234, PR China;Department of Mathematics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234, PR China
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

A class of high order continuous block implicit hybrid one-step methods has been proposed to solve numerically initial value problems for ordinary and delay differential equations. The convergence and A"@w-stability of the continuous block implicit hybrid methods for ordinary differential equations are studied. Alternative form of continuous extension is constructed such that the block implicit hybrid one-step methods can be used to solve delay differential equations and have same convergence order as for ordinary differential equations. Some numerical experiments are conducted to illustrate the efficiency of the continuous methods.