scholarly journals Double Laplace Decomposition Method and Finite Difference Method of Time-fractional Schrödinger Pseudoparabolic Partial Differential Equation with Caputo Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Mahmut Modanli ◽  
Bushra Bajjah
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Caputo Derivative ◽  
Decomposition Method ◽  
Linear Time ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Partial Differential ◽  
Laplace Decomposition Method

In this paper, an initial-boundary value problem for a one-dimensional linear time-dependent fractional Schrödinger pseudoparabolic partial differential equation with Caputo derivative of order α ∈ 0,1 is being considered. Two strong numerical methods are employed to acquire the solutions to the problem. The first method used is the double Laplace decomposition method where closed-form solutions are obtained for any α ∈ 0,1 . As the second method, the implicit finite difference scheme is applied to obtain the approximate solutions. To clarify the performance of these two methods, numerical results are presented. The stability of the problem is also investigated.

Existence Theorem for the Initial-Boundary Value Problem for a Singular Parabolic Partial Differential Equation

1972 ◽  
Vol 15 (2) ◽  
pp. 229-234
Author(s):  
Julius A. Krantzberg
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Image Position ◽  
Initial Boundary Value

We consider the initial-boundary value problem for the parabolic partial differential equation1.1in the bounded domain D, contained in the upper half of the xy-plane, where a part of the x-axis lies on the boundary B(see Fig.1).

Laplace Decomposition Method to Study Solitary Wave Solutions of Coupled Nonlinear Partial Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Arun Kumar ◽  
Ram Dayal Pankaj
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equation ◽  
Weak Nonlinearity ◽  
Partial Differential ◽  
New Approach ◽  
Laplace Decomposition Method

Analytical and numerical solutions are obtained for coupled nonlinear partial differential equation by the well-known Laplace decomposition method. We combined Laplace transform and Adomain decomposition method and present a new approach for solving coupled Schrödinger-Korteweg-de Vries (Sch-KdV) equation. The method does not need linearization, weak nonlinearity assumptions, or perturbation theory. We compared the numerical solutions with corresponding analytical solutions.

scholarly journals On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method

2020 ◽  
Vol 5 (1) ◽  
pp. 163-170 ◽  
Author(s):  
Mahmut Modanli ◽  
Ali Akgül
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Partial Differential ◽  
Problem Stability ◽  
The Stability ◽  
Initial Boundary Value

AbstractThe exact solution is calculated for fractional telegraph partial differential equation depend on initial boundary value problem. Stability estimates are obtained for this equation. Crank-Nicholson difference schemes are constructed for this problem. The stability of difference schemes for this problem is presented. This technique has been applied to deal with fractional telegraph differential equation defined by Caputo fractional derivative for fractional orders α = 1.1, 1.5, 1.9. Numerical results confirm the accuracy and effectiveness of the technique.

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