Numerical approximation for two-dimensional neutral parabolic differential equations with delay. (2nd January 2016) - Zhang, Qifeng; Ran, Maohua; Li, Zhong
Abstract : In this article, an effective compact difference scheme is proposed to solve two-dimensional neutral delay parabolic differential equations (NDPDEs). Concrete and detailed derivation of the scheme is given. The unique solvability and unconditional stability are obtained. Several numerical experiments indicate that the scheme has second-order accuracy in temporal direction and fourth-order accuracy in spatial direction in the sense of -norms and -norms. All procedures given in the paper can be extended to NDPDEs in three-dimensional case.