A Dimensional Splitting of ETD Schemes for Reaction-Diffusion Systems

AbstractNovel dimensional splitting techniques are developed for ETD Schemes which are second-order convergent and highly efficient. By using the ETD-Crank-Nicolson scheme we show that the proposed techniques can reduce the computational time for nonlinear reaction-diffusion systems by up to 70%. Numerical tests are performed to empirically validate the superior performance of the splitting methods.

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A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting

Journal of Computational Physics ◽

10.1016/j.jcp.2020.109490 ◽

2020 ◽

Vol 415 ◽

pp. 109490 ◽

Cited By ~ 1

Author(s):

E.O. Asante-Asamani ◽

A. Kleefeld ◽

B.A. Wade

Keyword(s):

Reaction Diffusion ◽

Second Order ◽

Exponential Time ◽

Reaction Diffusion Systems ◽

Exponential Time Differencing ◽

Diffusion Systems ◽

Dimensional Splitting ◽

Linear Reaction ◽

Non Linear

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CAS WAVELETS METHOD TO SOLVE REACTION-DIFFUSION SYSTEM AND COMPARE IT WITH (G.F.E) METHOD

Periódico Tchê Química ◽

10.52571/ptq.v17.n35.2020.91_salim_pgs_1110_1123.pdf ◽

2020 ◽

Vol 17 (35) ◽

pp. 1110-1123

Author(s):

Badran Jasim SALIM ◽

Oday Ahmed JASIM

Keyword(s):

Steady State ◽

Finite Elements ◽

Reaction Diffusion ◽

Partial Differential ◽

Reaction Diffusion Systems ◽

Time Frequency ◽

Nonlinear Reaction ◽

Diffusion Systems ◽

Cas Wavelets ◽

Steady State Solutions

Wavelet analysis plays a prominent role in various fields of scientific disciplines. Mainly, wavelets are very successfully used in signal analysis for waveform representation and segmentation, time-frequency analysis, and fast algorithms in the propagation equations and reaction. This research aimed to guide researchers to use Cos and Sin (CAS) to approximate the solution of the partial differential equation system. This method has been successfully applied to solve a coupled system of nonlinear Reaction-diffusion systems. It has been shown CAS wavelet method is quite capable and suited for finding exact solutions once the consistency of the method gives wider applicability where the main idea is to transform complex nonlinear partial differential equations into algebraic equation systems, which are easy to handle and find a numerical solution for them. By comparing the numerical solutions of the CAS and Galerkin finite elements methods, the answer of nonlinear Reaction-diffusion systems using the CAS wavelets for all tˆ and x values is accurate, reliable, robust, promising, and quickly arrives at the exact solution. When parameters 𝜀1 𝑎𝑛𝑑 𝜀2 are growing and with L decreasing, then the CAS method converges to steady-state solutions quickly (the less L, the more accurate the solution). It is converging towards steady-state solutions faster than and loses steps over time. Moreover, the results also show that the solution of the CAS wavelets is more reliable and faster compared to the Galerkin finite elements (G.F.E).

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