Numerical approximation for two-dimensional neutral parabolic differential equations with delay

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.

Keywords:

• Two-dimensional neutral delay parabolic differential equations
• compact difference scheme
• solvability
• unconditional stability

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Natural Science Foundation of China [grant number 11501514]; Natural Sciences Foundation of Zhejiang Province [grant number LQ16A010007]; Zhejiang Province Ministry of Education [grant number Y201533134]; and School Initiation Funds in ZSTU [grant number 11432932611470].