Solving a system of fourth‐order obstacle boundary value problems by differential transform method

Kybernetes ◽  
2008 ◽  
Vol 37 (2) ◽  
pp. 315-325
Author(s):  
Shaher Momani ◽  
Vedat Suat Ertürk
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform

scholarly journals H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform Method

2021 ◽  
Vol 5 (4) ◽  
pp. 166
Author(s):  
Shahram Rezapour ◽  
Brahim Tellab ◽  
Chernet Tuge Deressa ◽  
Sina Etemad ◽  
Kamsing Nonlaopon
Keyword(s):  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Differential Transform Method ◽  
Coupled Systems ◽  
Existence Theory ◽  
Transform Method ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Differential Transform ◽  
Generalized Differential

This paper is devoted to generalizing the standard system of Navier boundary value problems to a fractional system of coupled sequential Navier boundary value problems by using terms of the Caputo derivatives. In other words, for the first time, we design a multi-term fractional coupled system of Navier equations under the fractional boundary conditions. The existence theory is studied regarding solutions of the given coupled sequential Navier boundary problems via the Krasnoselskii’s fixed-point theorem on two nonlinear operators. Moreover, the Banach contraction principle is applied to investigate the uniqueness of solution. We then focus on the Hyers–Ulam-type stability of its solution. Furthermore, the approximate solutions of the proposed coupled fractional sequential Navier system are obtained via the generalized differential transform method. Lastly, the results of this research are supported by giving simulated examples.

scholarly journals Differential Transform Technique for Higher Order Boundary Value Problems

2015 ◽  
Vol 9 (13) ◽  
pp. 224 ◽  
Author(s):  
Abiodun Adegboyega Opanuga ◽  
Hilary I. Okagbue ◽  
Sunday O. Edeki ◽  
Olasunmbo O. Agboola
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Higher Order ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform

This paper presents the approximate solution of higher order boundary value problems by differential transform method. Two examples are considered to illustrate the efficiency of this method. The results converge rapidly to the exact solution and are shown in tables and graphs.

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