University of TabrizComputational Methods for Differential Equations2345-39828220200401The numerical solution of Fisher equation: A nonstandard finite difference in conjunction with Richtmyer formula330346996310.22034/cmde.2020.27907.1379ENFanooshIzadiDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
Lahijan Branch, Islamic Azad University, Lahijan, Iran.HashemSaberiNajafiDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
Lahijan Branch, Islamic Azad University, Lahijan, Iran.0000-0001-6723-8126A.H.Refahi SheikhaniDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
Lahijan Branch, Islamic Azad University, Lahijan, Iran.0000-0003-1664-5471Journal Article20180613A nonstandard finite-difference (NSFD) scheme for Fisher’s Equation by using Richtmyer’s (3, 1, 1) implicit formula has been presented, in this work. On nonstandard finite-difference scheme, two special cases of Richtmyer formula have been applied. The suitable functions in the denominator fraction of our NSFD scheme have been replaced to guarantee the highly accurate of the approximation. Furthermore, the analyses of stability, convergence, consistency for the NSFD method, have been provided. By calculating the absolute error, the comparison of these methods has been presented in some Examples and the results have shown that the error of our NSFD scheme is lower than the others. Finally, a comparison of these methods and the differential quadrature method (DQM) to solve the Fisher’s Equation reveals that these techniques work better and give highly accurate results.https://cmde.tabrizu.ac.ir/article_9963_68fcb20d5152cbc8f4ff148a8a57e978.pdf