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A linearized compact θ-method for 2D semi-linear generalized pantograph-reaction–diffusion equations

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  • Jin, Zhixiang
  • Zhang, Chengjian

Abstract

This paper deals with the numerical solution of the initial–boundary value problem of 2D semi-linear generalized pantograph-reaction–diffusion equations (PRDEs). By combining a linearized compact method, θ-method, composite trapezoidal rule and the fully-geometric grid in temporal direction, a new numerical method is proposed for solving the problem. Under the suitable conditions, the proposed method is proved to be globally stable, and convergent of order two (resp. one) in time when θ=12 (resp. θ≠12) and order four in space. In the end, some numerical experiments are provided to confirm the computational effectiveness of the method and the derived theoretical results.

Suggested Citation

  • Jin, Zhixiang & Zhang, Chengjian, 2026. "A linearized compact θ-method for 2D semi-linear generalized pantograph-reaction–diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 246(C), pages 175-187.
    • Handle: RePEc:eee:matcom:v:246:y:2026:i:c:p:175-187
    DOI: 10.1016/j.matcom.2026.01.034
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    References listed on IDEAS

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    1. Lekomtsev, Andrey & Pimenov, Vladimir, 2015. "Convergence of the scheme with weights for the numerical solution of a heat conduction equation with delay for the case of variable coefficient of heat conductivity," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 83-93.
    2. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays," Mathematics, MDPI, vol. 11(3), pages 1-25, January.
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