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Fourth order computational spline method for two-parameter singularly perturbed boundary value problem

Kambampati Satyanarayana, Emineni Siva Prasad, Reddy M. Chenna Krishna, Kolloju Phaneendra

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 4

79--93

EN

The current research work considers a two-parameter singularly perturbed two-point boundary value problem. Here, we suggest a computational scheme derived by using an exponential spline for the numerical solution of the problem on a uniform mesh. The proposed numerical scheme is analyzed for convergence and an accuracy of O(h4) is achieved. Numerical experiments are considered to validate the efficiency of the spline method, and compared comparison with the existing method to prove the superiority of the proposed scheme.

2

Computational scheme for a differential difference equation with a large delay in convection term

Erla Srinivas, Kolloju Phaneendra

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 2

34--48

EN

A computational scheme for the solution of layer behaviour differential equation involving a large delay in the derivative term is devised using numerical integration. If the delay is greater than the perturbation parameter, the layer structure of the solution is no longer preserved, and the solution oscillates. A numerical method is devised with the support of a specific kind of mesh in order to reduce the error and regulate the layered structure of the solution with a fitting parameter. The scheme is discussed for convergence. The maximum errors in the solution are tabulated and compared to other methods in the literature to verify the accuracy of the numerical method. Using this specific kind of mesh with and without the fitting parameter, we also studied the layer and oscillatory behavior of the solution with a large delay.

3

Difference scheme for differential-difference problems with small shifts arising in computational model of neuronal variability

Kodipaka Mamatha, Emineni Siva Prasad, Kolloju Phaneendra

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 1

91--106

EN

The solution of differential-difference equations with small shifts having layer behaviour is the subject of this study. A difference scheme is proposed to solve this equation using a non-uniform grid. With the non-uniform grid, finite - difference estimates are derived for the first and second-order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the tridiagonal system algorithm. Convergence of the scheme is examined. Various numerical simulations are presented to demonstrate the validity of the scheme. In contrast to other techniques, maximum errors in the solution are organized to support the method. The layer behaviour in the solutions of the examples is depicted in graphs.

4

Computational approach to solving a layered behaviour differential equation with large delay using quadrature scheme

Pandi A., Mudavath Lalu, Kolloju Phaneendra

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 4

117--137

EN

This paper deals with the computational approach to solving the singularly perturbed differential equation with a large delay in the differentiated term using the two-point Gaussian quadrature. If the delay is bigger than the perturbed parameter, the layer behaviour of the solution is destroyed, and the solution becomes oscillatory. With the help of a special type mesh, a numerical scheme consisting of a fitting parameter is developed to minimize the error and to control the layer structure in the solution. The scheme is studied for convergence. Compared with other methods in the literature, the maximum defects in the approach are tabularized to validate the competency of the numerical approach. In the suggested technique, we additionally focused on the effect of a large delay on the layer structure or oscillatory behaviour of the solutions using a special form of mesh with and without a fitting parameter. The effect of the fitting parameter is demonstrated in graphs to show its impact on the layer of the solution.