具有多个弱奇异核的三维非线性PIDEs的分级网格高阶紧致CN-ADI格式

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-07-24 DOI:10.1016/j.aml.2025.109697

Tianyuan Liu , Haixiang Zhang , Song Wang

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引用次数: 0

摘要

针对具有多个弱奇异核的三维非线性偏积分微分方程（PIDEs），提出了一种新的紧凑的Crank-Nicolson交替方向隐式差分格式。采用梯形积积分（PI）规则对Riemann-Liouville （R-L）积分项进行离散化，并通过二阶泰勒展开对非线性项进行逼近。采用CN公式对时间导数进行离散化，并采用梯度网格解决t=0附近的弱奇异性。给出了该方案的严格误差估计，并进行了全面的数值实验，验证了理论结果。

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A new high-order compact CN-ADI scheme on graded meshes for three-dimensional nonlinear PIDEs with multiple weakly singular kernels

This study presents a novel compact Crank–Nicolson alternating direction implicit (CN-ADI) difference scheme tailored for three-dimensional (3D) nonlinear partial integro-differential equations (PIDEs) with multiple weakly singular kernels. The Riemann–Liouville (R-L) integral terms are discretized using the trapezoidal product integration (PI) rule, and the nonlinear term are approximated via second-order Taylor expansion. The time derivative is discretized using the CN formula, and the graded meshes are employed to address the weak singularity near

t = 0

. The rigorous error estimates for the proposed scheme are derived, and comprehensive numerical experiments validate the theoretical results.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.