Numerical solution of time dependent nonlinear partial differential equations using a novel block method coupled with compact finite difference schemes

Mehta, Akansha; Singla, Rajat; Ramos, Higinio

doi:10.1007/s40314-023-02345-3

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…The compact finite difference block technique is denoted by CFDBT and is described in [35]. This method involves approximating the derivatives of time-dependent partial differential equations using finite difference approximations in combination with the block method.…”

Section: Numerical Examples and Comparisonsmentioning

confidence: 99%

“…As a first numerical example, we consider the NFNE in Equation (1). The equation is subject to the following initial condition, as presented in [34,35]:…”

Section: Numerical Examplementioning

confidence: 99%

“…Consider a class of NFNE in Equation (1), which belongs to the class of stiff test problems as reported by [35,37]. The problem is given by…”

Section: Numerical Examplementioning

confidence: 99%

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A New Two-Step Hybrid Block Method for the FitzHugh–Nagumo Model Equation

Rufai,

Kosti,

Anastassi

et al. 2023

Mathematics

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This paper presents an efficient two-step hybrid block method (ETHBM) to obtain an approximate solution to the FitzHugh–Nagumo problem. The considered partial differential equation model problems are semi-discretized, reducing them to equivalent ordinary differential equations using the method of lines. In order to evaluate the effectiveness of the proposed ETHBM, three numerical examples are presented and compared with the results obtained through existing methods. The results demonstrate that the proposed ETHBM produces more efficient results than some other numerical approaches in the literature.

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Section: Numerical Examples and Comparisonsmentioning

confidence: 99%

“…As a first numerical example, we consider the NFNE in Equation (1). The equation is subject to the following initial condition, as presented in [34,35]:…”

Section: Numerical Examplementioning

confidence: 99%

See 1 more Smart Citation

A New Two-Step Hybrid Block Method for the FitzHugh–Nagumo Model Equation

Rufai,

Kosti,

Anastassi

et al. 2023

Mathematics

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An optimized hybrid block method for solving nonlinear singularly perturbed problems using non-uniform Jain-type meshes

Bisheh-Niasar,

Khaziravi,

Ramos

2024

International Journal of Computer Mathematics

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Solving scalar reaction diffusion equations with cubic non-linearity having time-dependent coefficients by the wavelet method of lines

Khan,

Ghafoor,

Khan

et al. 2024

NHM

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This paper aims to conduct the numerical solutions of the scalar reaction diffusion model with cubic non-linearity having constant and time-dependent coefficients. The proposed method is hybrid in nature in which Haar wavelets are used to approximate the spatial derivatives and the Runge-Kutta (RK) routines are used to solve the resultant system of ordinary differential equations. We illustrate the applicability and efficiency of the proposed method by computing $ L_2 $, $ L_{\infty} $, and $ L_{rms} $ error estimates for various test models. The numerical accuracy and stability of the Haar wavelet-based method of lines for solving the scaler reaction-diffusion model provides further insight into the use of this scheme for model equations across various disciplines.

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Numerical solution of time dependent nonlinear partial differential equations using a novel block method coupled with compact finite difference schemes

Cited by 3 publications

References 23 publications

A New Two-Step Hybrid Block Method for the FitzHugh–Nagumo Model Equation

A New Two-Step Hybrid Block Method for the FitzHugh–Nagumo Model Equation

An optimized hybrid block method for solving nonlinear singularly perturbed problems using non-uniform Jain-type meshes

Solving scalar reaction diffusion equations with cubic non-linearity having time-dependent coefficients by the wavelet method of lines

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