Numerical Analysis of Discrete Laplace Transform for Higher Order Cosine Function and Applications in Initial Value Problem

Numerical Analysis of Discrete Laplace Transform for Higher Order Cosine Function and Applications in Initial Value Problem

Authors

  • B. Govindan, T. Sathinathan, S. John Borg, Sandra Pinelas, M. Meganathan

Keywords:

Difference equation, Difference operator, Laplace transform, Initial value problem

Abstract

In this research work, we obtain Discrete Laplace Transform(DILAT) of higher order cosine functions and using this DILAT results by employing Initial Value Problems to get applications in the field of physical sciences. Also we present several theorems and examples to illustrate our findings by using MATLAB.

References

Agarwal RP and Wong PJY, Advanced Topics in Difference equations, Kluwer, Dordrecht, 1997.

Agarwal RP, Difference Equations and Inequalities, Marcel Dekkar, New York, 2000.

R. Anguelov, Spline-Fourier approximation of discontinuous waves, J. Univ. Comput. Sci. 4(2), 1998.

Ernst Hairer and Gerhard Wanner, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations Society for Industrial and Applied Mathematics, 1980.

Govindan B, Nandhini M and Meganathan M, Generalized Discrete Finite Half Range Fourier Series, Advances in Math ematics: Scientific Journal, 1225-1237, 2021.

Maria Susai Manuel M, Britto Antony Xavier B and Thandapani E, Theory of Generalized Difference Operator and its Applications, Far East Journal of Mathematical sciences, 20(2)(2006),163-171.

Maria Susai Manuel M, Britto Antony Xavier B, Chandrasekar V and Pugalarasu R, Theory and applications of the Generalized Difference Operator of the n th Kind(Part-I), Demonstratio Mathematica, Vol.45,no.1, pp.95-106,2012.

M. Meganathan, G. Britto Antony Xavier and T. Abdeljawad, Modeling with Fractional Laplace Transform by hdifference Operator, Progress in Fractional Differentiation and Applications, 2020, 6(4).

Meganathan M, T.Abdeljawad, Fahd Jarad and G Britto Antony Xavier, n-dimensional Fractional Frequency Laplace transform by Inverse Difference Operator, Mathematical Problems in Engineering, Volume 2020, Article ID 6529698.

Sandra Pinelas, M. Meganathan and G. Britto Antony Xavier, Fractional Frequency Laplace Transform by In verse Difference Operator with Shift Value, Open Journal of Mathematical Sciences (OMS), 2019, 3, 121-128; doi:10.30538/oms2019.0055.

Ronald E.Mickens, Difference Equations, Van Nostrand Reinhold Company, New York, 1990.

Saber N.Elaydi, An Introduction to Difference Equations,2/e Springer Verlag, 1999.

Steven W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing, Second Edition, California Technical Publishing San Diego, California, 1999.

William E Boyce and Richard C. DiPrima,Elementary Differential Equations and Boundary Value Problems Wiley, 1980.

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Published

2023-12-30

Issue

Section

Articles

How to Cite

Numerical Analysis of Discrete Laplace Transform for Higher Order Cosine Function and Applications in Initial Value Problem. (2023). Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 183-192. https://doi.org/10.17762/atnaa.v7.i5.334