A-high-order accuracy explicit difference scheme for solving the equation of two-dimensional parabolic type

Abstract

In this paper, a three explicit difference shcemes with high order accuracy for solving the equations of two-dimensional parabolic type is proposed. The stability condition is % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2% da9maalyaabaGaeyiLdqKaamiDaaqaaiabgs5aejaadIhadaahaaWc% beqaaiaaikdaaaGccqGH9aqpdaWcgaqaaiabgs5aejaadshaaeaacq% GHuoarcaWG5bWaaWbaaSqabeaacaaIYaaaaaaakmaalyaabaGaaGym% aaqaaiaaigdaaaaaaaaa!4616!\[r = {{\Delta t} \mathord{\left/ {\vphantom {{\Delta t} {\Delta x^2 = {{\Delta t} \mathord{\left/ {\vphantom {{\Delta t} {\Delta y^2 }}} \right. \kern-\nulldelimiterspace} {\Delta y^2 }}{1 \mathord{\left/ {\vphantom {1 1}} \right. \kern-\nulldelimiterspace} 1}}}} \right. \kern-\nulldelimiterspace} {\Delta x^2 = {{\Delta t} \mathord{\left/ {\vphantom {{\Delta t} {\Delta y^2 }}} \right. \kern-\nulldelimiterspace} {\Delta y^2 }}⩽{1 \mathord{\left/ {\vphantom {1 1}} \right. \kern-\nulldelimiterspace} 1}}}\] and the truncation error is O(Δt²+Δx⁴).