Compact block boundary value methods for semi-linear delay-reaction-diffusion equations with algebraic constraints

摘要

In the present paper, we study a class of linear approximation methods for solving semi-linear delay-reaction-diffusion equations with algebraic constraint (SDEACs). By combining a fourth-order compact difference scheme with block boundary value methods (BBVMs), a class of compact block boundary value methods (CBBVMs) for SDEACs are suggested. It is proved under some suitable conditions that the CBBVMs are convergent of order 4 in space and orderpin time, wherepis the local order of the used BBVMs, and are globally stable. With several numerical experiments for Fisher equation with delay and algebraic constraint, the computational effectiveness and theoretical results of CBBVMs are further illustrated.