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.

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.

ORDER AND CONVERGENCE OF THE ENHANCED 3-POINT FULLY IMPLICIT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING INITIAL VALUE PROBLEM

2021 ◽  
Vol 5 (2) ◽  
pp. 442-446
Author(s):  
Muhammad Abdullahi ◽  
Hamisu Musa
Keyword(s):  
Initial Value Problem ◽  
Initial Value Problems ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Differentiation Formula ◽  
Stiff Initial Value Problems ◽  
First Order ◽  
Backward Differentiation Formula ◽  
Fully Implicit ◽  
Necessary And Sufficient

This paper studied an enhanced 3-point fully implicit super class of block backward differentiation formula for solving stiff initial value problems developed by Abdullahi & Musa and go further to established the necessary and sufficient conditions for the convergence of the method. The method is zero stable, A-stable and it is of order 5. The method is found to be suitable for solving first order stiff initial value problems

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.

scholarly journals Numerical solutions of nonstandard first order initial value problems

1992 ◽  
Vol 5 (1) ◽  
pp. 69-82 ◽  
Author(s):  
M. Venkatesulu ◽  
P. D. N. Srinivasu
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Unique Solution ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Initial Value ◽  
First Order ◽  
Physical Phenomena

Differential equations of the form y′=f(t,y,y′), where f is not necessarily linear in its arguments, represent certain physical phenomena and are known for quite some time. The well known Clairut's and Chrystal's equations fall into this category. Earlier, we established the existence of a (unique) solution of the nonstandard initial value problem (NSTD IV P) y′=f(t,y,y′), y(t0)=y0 under certain natural hypotheses on f. In this paper we present some first order convergent numerical methods for finding the approximate solutions of the NST D I V Ps.

Continuous One Step Linear Multi-Step Hybrid Block Method for the Solution of First Order Linear and Nonlinear Initial Value Problem of Ordinary Differential Equations

2021 ◽  
Author(s):  
Kamoh Nathaniel ◽  
Kumleng Geoffrey ◽  
Sunday Joshua
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Algebraic Equations ◽  
Initial Value ◽  
Closed Form Solutions ◽  
First Order ◽  
One Step ◽  
Collocation Approach

In this paper, a collocation approach for solving initial value problem of ordinary differential equations (ODEs) of the first order is presented. This approach consists of reducing the problem to a set of linear multi-step algebraic equations by approximating the ODE with a shifted Legendre polynomial basis function to determine the unknown constants. The proposed method is simple and efficient; it approximates the solutions very closely to the closed form solutions. Some problems were considered using Maple Software to illustrate the simplicity, efficiency and accuracy of the method. The results obtained revealed that the hybrid method can be suitable candidate for all forms of first order initial value problems of ordinary differential equations.

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