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 FORMULATION OF BLOCK SCHEMES WITH LINEAR MULTISTEP METHOD FOR THE APPROXIMATION OF FIRST-ORDER IVPS

2020 ◽  
Vol 4 (3) ◽  
pp. 313-322
Author(s):  
Sunday Obomeviekome Imoni ◽  
D. I. Lanlege ◽  
E. M. Atteh ◽  
J. O. Ogbondeminu
Keyword(s):  
Basis Function ◽  
Initial Value Problems ◽  
Hermite Polynomials ◽  
Multistep Method ◽  
Linear Multistep Method ◽  
Initial Value ◽  
Numerical Examples ◽  
First Order ◽  
Block Scheme ◽  
Multi Step Methods

ABSTRACT In this paper, formulation of an efficient numerical schemes for the approximation first-order initial value problems (IVPs) of ordinary differential equations (ODE) is presented. The method is a block scheme for some k-step linear multi-step methods (and) using the Hermite Polynomials a basis function. The continuous and discrete linear multi-step methods (LMM) are formulated through the technique of collocation and interpolation. Numerical examples of ODE have been examined and results obtained show that the proposed scheme can be efficient in solving initial value problems of first order ODE.

An L∞-error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems

2015 ◽  
Vol 5 (4) ◽  
pp. 301-311 ◽  
Author(s):  
Lijun Yi
Keyword(s):  
Error Estimate ◽  
Galerkin Method ◽  
Error Bound ◽  
Initial Value Problems ◽  
Initial Value ◽  
Numerical Examples ◽  
Time Stepping ◽  
Theoretical Results

AbstractThe h-p version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An L∞-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.

scholarly journals Numerical inversion of the Laplace transform

1999 ◽  
Vol 110 (23) ◽  
pp. 11176-11186 ◽  
Author(s):  
Bruno Hüpper ◽  
Eli Pollak
Keyword(s):  
Laplace Transform ◽  
Numerical Inversion ◽  
The Laplace Transform
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