An easy to implement linearized numerical scheme for fractional reaction–diffusion equations with a prehistorical nonlinear source function

Omran, A.K.; Zaky, Mahmoud A.; Hendy, Ahmed S.; Пименов, В. Г.

doi:10.1016/j.matcom.2022.04.014

Cited by 5 publications

(2 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Motivated by the highly precise approximations in the numerical approximation of differential and integral equations using pseudospectral schemes, [28][29][30][31][32][33][34][35][36][37][38] we present tanh-Jacobi pseudospectral scheme for the nonlinear Schrödinger equations on an infinite domain. The following are the main contributions of this work:…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the highly precise approximations in the numerical approximation of differential and integral equations using pseudospectral schemes, 28–38 we present tanh‐Jacobi pseudospectral scheme for the nonlinear Schrödinger equations on an infinite domain. The following are the main contributions of this work: In the first part, we build classes of tanh orthogonal functions by applying a tanh mapping to Jacobi polynomials.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain

Mostafa

Zaky

Hafez

et al. 2022

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

We present a class of orthogonal functions on infinite domain based on Jacobi polynomials. These functions are generated by applying a tanh transformation to Jacobi polynomials. We construct interpolation and projection error estimates using weighted pseudo‐derivatives tailored to the involved mapping. Then, using the nodes of the newly introduced tanh Jacobi functions, we develop an efficient spectral tanh Jacobi collocation method for the numerical simulation of nonlinear Schrödinger equations on the infinite domain without using artificial boundary conditions. The applicability and accuracy of the solution method are demonstrated by two numerical examples for solving the nonlinear Schrödinger equation and the nonlinear Ginzburg–Landau equation.

show abstract