Section 85: The delta function and its use in initial value problems with the Laplace transform

2004 ◽  
pp. 701-706
Keyword(s):  
Laplace Transform ◽  
Initial Value Problems ◽  
Delta Function ◽  
Initial Value ◽  
The Laplace Transform

A Technique for Increasing the Accuracy of the Numerical Inversion of the Laplace Transform With Applications

1973 ◽  
Vol 40 (4) ◽  
pp. 1110-1112 ◽  
Author(s):  
B. S. Berger ◽  
S. Duangudom
Keyword(s):  
Laplace Transform ◽  
Initial Value Problems ◽  
Numerical Inversion ◽  
Initial Value ◽  
Numerical Examples ◽  
Oscillatory Function ◽  
Higher Order Terms ◽  
The Laplace Transform ◽  
Image Function ◽  
Inversion Techniques

A technique is introduced which extends the range of useful approximation of numerical inversion techniques to many cycles of an oscillatory function without requiring either the evaluation of the image function for many values of s or the computation of higher-order terms. The technique consists in reducing a given initial value problem defined over some interval into a sequence of initial value problems defined over a set of subintervals. Several numerical examples demonstrate the utility of the method.

scholarly journals Analysis of Multiterm Initial Value Problems with Caputo–Fabrizio Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Mohammed Al-Refai ◽  
Muhammed Syam
Keyword(s):  
Laplace Transform ◽  
Fractional Derivative ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Initial Value ◽  
The Laplace Transform ◽  
Necessary And Sufficient

In this paper, we discuss the solvability of a class of multiterm initial value problems involving the Caputo–Fabrizio fractional derivative via the Laplace transform. We derive necessary and sufficient conditions to guarantee the existence of solutions to the problem. We also obtain the solutions in closed forms. We present two examples to illustrate the validity of the obtained results.

scholarly journals Solving Fractional Difference Equations Using the Laplace Transform Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Li Xiao-yan ◽  
Jiang Wei
Keyword(s):  
Laplace Transform ◽  
Difference Equations ◽  
Initial Value Problems ◽  
Initial Value ◽  
Laplace Transform Method ◽  
Fractional Difference ◽  
Transform Method ◽  
Fractional Difference Equations ◽  
The Laplace Transform ◽  
Linear And Nonlinear

We discuss the Laplace transform of the Caputo fractional difference and the fractional discrete Mittag-Leffer functions. On these bases, linear and nonlinear fractional initial value problems are solved by the Laplace transform method.

scholarly journals Soution of fuzzy initial value problems by fuzzy Laplace transform

10.29007/pnq2 ◽  
2018 ◽  
Author(s):  
Komal Patel ◽  
Narendrasinh Desai
Keyword(s):  
Laplace Transform ◽  
Initial Value Problem ◽  
Level Sets ◽  
Initial Value Problems ◽  
Initial Value ◽  
Generalized Differentiability ◽  
Strongly Generalized Differentiability ◽  
Fuzzy Laplace Transform ◽  
Mathematica Software

In this paper we propose a fuzzy Laplace transform to solve fuzzy initial value problem under strongly generalized differentiability concept. The fuzzy Laplace transform of derivative was used to solve Nth-order fuzzy initial value problem. To illustrate applicability of proposed method we plot graphs for different values of r -level sets by using Mathematica Software.

Extension of the Initial Value Theorem

1978 ◽  
Vol 15 (3) ◽  
pp. 237-241
Author(s):  
A. Henderson
Keyword(s):  
Laplace Transform ◽  
Initial Value ◽  
The Laplace Transform ◽  
Higher Derivatives ◽  
The Moment

A formula is derived which gives the value of the first and all higher derivatives at the moment t = 0+ directly from the Laplace transform.

Solutions of the Singular IVPs of Lane-Emden type equations by combining Laplace transformation and perturbation technique

2018 ◽  
Vol 7 (4) ◽  
pp. 273-278 ◽  
Author(s):  
Hossein Aminikhah
Keyword(s):  
Laplace Transform ◽  
Efficient Method ◽  
Initial Value Problems ◽  
Laplace Transformation ◽  
Perturbation Methods ◽  
Perturbation Technique ◽  
Initial Value ◽  
Homotopy Perturbation ◽  
Polynomial Series ◽  
Linear And Nonlinear

AbstractIn this paper, we propose an efficient method to solve linear and nonlinear singular initial value problems of Lane-Emden type equations by combining Laplace transformation and homotopy perturbation methods. The method is based upon Laplace transform, polynomial series and perturbation technique. Several examples, including some well-known Lane-Emden problems, are presented to show the ability and accuracy of the modify method.

scholarly journals On Solution of First Order Initial Value Problems using Laplace Transform in Fuzzy Environment

2021 ◽  
Vol 7 (2) ◽  
pp. 21-29
Author(s):  
Abubakar Terrang ◽  
◽  
Awumtiya Isa ◽  
Felix Bakare ◽  
Patience Iliya ◽  
...  
Keyword(s):  
Laplace Transform ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Initial Value ◽  
Laplace Transform Method ◽  
Transform Method ◽  
First Order ◽  
Fuzzy Environment ◽  
Fuzzy Function

This study aimed at solving a nonhomogeneous linear first order initial value problem by means of Laplace transform method in fuzzy environment. The conditions for a fuzzy function to be H−differentiable and gH−differentiability are well established. Finally, example is constructed to test the applicability or otherwise of the established results.

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