A Computational Scheme for 1D Time-Dependent Singularly Perturbed Parabolic Differential-Difference Equations.
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| Title: | A Computational Scheme for 1D Time-Dependent Singularly Perturbed Parabolic Differential-Difference Equations. |
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| Authors: | Prasad, E. Siva1 (AUTHOR) emineni@yahoo.co.in, Phaneendra, K.2 (AUTHOR) kollojuphaneendra@yahoo.co.in |
| Source: | Computational Mathematics & Mathematical Physics. Feb2025, Vol. 65 Issue 2, p236-251. 16p. |
| Subjects: | Differential-difference equations, Taylor's series, Euler method, Discretization methods, Splines |
| Abstract: | In this research, we proposed a fitted numerical scheme for time-dependent singularly perturbed parabolic equations with small retarded terms in the reaction terms. When the delay and advanced terms are of small order of perturbation, Taylor's series expansion is used to approximate delay terms. The resulting equations is solved by using the classical backward Euler method for the discretization of time variable and the adaptive cubic spline method in spatial discretize the variables on a uniform mesh. The suggested numerical technique is shown to be a parameter uniformly convergent of first order in time and second order in spatial direction. Numerical tests are given to validate the effectiveness of the adaptive cubic spline method, as well as to validate theoretical investigations and compare the numerical results with the other methods available in the literature. It is observed that the suggested method produces more accurate approximation findings and has a higher rate of convergence than the other methods currently accessible in the literature. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | In this research, we proposed a fitted numerical scheme for time-dependent singularly perturbed parabolic equations with small retarded terms in the reaction terms. When the delay and advanced terms are of small order of perturbation, Taylor's series expansion is used to approximate delay terms. The resulting equations is solved by using the classical backward Euler method for the discretization of time variable and the adaptive cubic spline method in spatial discretize the variables on a uniform mesh. The suggested numerical technique is shown to be a parameter uniformly convergent of first order in time and second order in spatial direction. Numerical tests are given to validate the effectiveness of the adaptive cubic spline method, as well as to validate theoretical investigations and compare the numerical results with the other methods available in the literature. It is observed that the suggested method produces more accurate approximation findings and has a higher rate of convergence than the other methods currently accessible in the literature. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 09655425 |
| DOI: | 10.1134/S096554252470194X |
