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- Title
Numerical Simulation of Generalized FitzHugh-Nagumo Equation by Shifted Chebyshev Spectral Collocation Method.
- Authors
Sharma, Seema; Prabhakar, Nidhi
- Abstract
The present study focuses on numerical simulation of generalized FitzHugh-Nagumo equation employing shifted Chebyshev spectral collocation method (SCSCM). The collocation method makes use of shifted Chebyshev polynomials for approximation of spatial variable and its derivatives, whereas, Chebyshev-Gauss-Lobatto points are employed for collocation purpose. The approximation of FitzHugh-Nagumo equation gives rise to a system of nonlinear ordinary differential equations (ODEs). The solution of this system of ODEs has been obtained by using Runge-Kutta scheme of order 4. The obtained numerical solutions are shown in graphical and tabular form. The convergence of SCSCM has been demonstrated as well. Further, to verify the efficiency and accuracy of the present method, the absolute, maximum absolute, root mean square and relative errors have been calculated for some examples of FitzHugh-Nagumo equation. The comparison of present numerical solutions with exact and approximate solutions obtained by other methods reveals that present method provides better accuracy.
- Subjects
STANDARD deviations; ORDINARY differential equations; NONLINEAR differential equations; POLYNOMIAL approximation; CHEBYSHEV polynomials; COLLOCATION methods
- Publication
IAENG International Journal of Applied Mathematics, 2024, Vol 54, Issue 7, p1371
- ISSN
1992-9978
- Publication type
Article