ESP Journal of Engineering & Technology Advancements |

© 2023 by ESP JETA |

Volume 3 Issue 2 |

Year of Publication : 2023 |

Authors : Jyoti V Dighole, Mangal P Kale |

:10.56472/25832646/JETA-V3I4P104 |

Jyoti V Dighole, Mangal P Kale, 2023. "Differential Transformation in Numerical Study: A Case Study Differentiability Equation" *ESP Journal of Engineering & Technology Advancements* 3(2): 35-38.

Differential equations play a crucial role in understanding many events in technology and generation. Transformation techniques are one of the numerical approaches that mathematicians have devised to provide a numerical solution of differential equations with the least amount of error. There is currently no transformation method that claims to solve the supplied differential equations numerically or accurately without error. Laplace remodel, Differential transform, crucial remodel procedure, and others are a few of the transformation techniques. Laplace remodel, one of the techniques utilised by scientists and researchers to solve their differential equations, is presented in this study. This study of 18 research publications on Laplace rework programmes shows how many academics have used this rework to obtain the accurate solutions to ordinary, partial, and fractional differential equations. The primary objective of this work is to give a literature review on the use of the Laplace transform.

[1] Aggarwal 2019 Laplace transform for convolution type linear Volterra intergral equation of second kind Journal of Advanced research in applied mathematics and statstics vol 4 pp 1-7

[2] Aggarwal 2018 Applications of Laplace Transform for solving Poulation Growth and Decay Problem International Journal of latest technology in Engeneering, Management and Applied sciences vol 7 pp 141-145

[3] Aggarwal 2019 Laplace Transform for the Solution of Abel's Transform Journal of Advanced Research in Applied Mathematics and Statstics vol 4 pp 8-15

[4] Bhairwa R 2019 Analytical solution of the Time Fractional Fisher equation by Laplace Transform Journal of Rajasthan Academy of Physical Sciences vol 17 pp 191-200

[5] Dhunde R 2015 Solution of linear partial integro differential equation using double laplace transform American Journal of Computational and Applied Mathematics vol 5 pp 7-10

[6] HE J 1999 Homotopy Perturbation Technique Computer methods in applied mechanics and engineering pp 257-262

[7] Hou J 2013 An Approximate Solution of non linear Fractional differential equation by Laplace Transform and Adomian Polynomials Journal of information and computational science vol 10 pp 213-222

[8] Liu J 2014 An analytic study on Fisher Equation by Homotopy perturbation mathod Journal of science and technology vol 11 p 975

[9] Jafari H 2006 An iterative method for solving non- linear functional equations Journal of mathematical analysis and applications vol 316 pp 753-763

[10] Khuri S 2001 A Laplace decomposition algorithm applied to class of non-linear differential equation Journal of applied mathematics vol 1 pp 141-155

[11] Kiymaz O 2009 An algorithm for solving intial value problems using Laplace Adomian Decompostion method Journal of Applied Mathematical Sciences vol 3 pp 1453-1459

[12] Kumar S 2012 A fraction model of diffusion equation and its analytical solution using Laplace Transform Scientia Iranica vol 19 pp 1117-1123

[13] Kumar S 2012 A fractional model of gas dynamics equations and its Analytical Approximate solution using Laplace Transform. Z. Naturforsch vol 67a pp 389 – 396

[14] Madani M 2010 Homotopy Perturbation Algorithm using Laplace Transformation Non-linear Sciences vol 1 pp 263-267

[15] Sharma SC 2015 Iterative Laplace Tranform method for solving fraction heat and wave equations Research Jounal of mathematical and statistical sciences vol 3 pp 4-9

[16] Shankar K 2015 An exact solution of Diffusion equation with boundary conditions by Pade- Laplace differential Transform method International Journal of mathematics and its applications vol 3 pp 1-8

[17] Sharma N 2019 Laplace Transform for the solution of first kind linear Volterra Integral equation Journal of advanced research in applied mathematics and statstics vol 4 pp 16-23

[18] Thorwe J 2012 Solving Partial Integro- DIfferential Equations using Laplace Transform Method American Journal of Computational and Applied Mathematics vol 2 pp 101-104

Laplace transform, Iterative method, Fisher equation, Diffusion equation, Partial integro differential equation, The equations of gas dynamics, Volterra integral equations, Abel's integral equation, Malthusian regulation of population increase