scholarly journals Solution of Parabolic Partial Differential Equations by Non-Polynomial Cubic Spline Technique

2021 ◽  
Vol 5 (3) ◽  
Author(s):  
Bilal Ahmad ◽  
Anjum Perviz ◽  
Muhammad Ozair Ahmad ◽  
Fazal Dayan
Keyword(s):  
Research Work ◽  
Numerical Test ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
The Novel ◽  
Parabolic Pdes ◽  
Partial Differential ◽  
Novel Technique ◽  
Engineering And Technology ◽  
Scientific Engineering

Parabolic partial differential equation having a great impact on our scientific, engineering and technology. Enormous research have been conducted for the solution of parabolic PDEs. . In this research work, we introduced a novel technique for the numerical solution of fourth order PDEs.  The novel technique is based upon the polynomial cubic cutting method (PCSM) was used with Adomian breakdown technique (ADM).The constraint for the alternative variables was decomposed by Edomian decomposition for the successive approximation. A numerical test problem of parabolic PDEs solved by purposed technique

The Solution of the Variable Coefficients Fourth-Order Parabolic Partial Differential Equations by the Homotopy Perturbation Method

2009 ◽  
Vol 64 (7-8) ◽  
pp. 420-430 ◽  
Author(s):  
Mehdi Dehghan ◽  
Jalil Manafian
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fourth Order ◽  
Homotopy Perturbation Method ◽  
Variable Coefficients ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Homotopy Perturbation

AbstractIn this work, the homotopy perturbation method proposed by Ji-Huan He [1] is applied to solve both linear and nonlinear boundary value problems for fourth-order partial differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solution to show the efficiency of the method. The results show that the homotopy perturbation method is of high accuracy and efficient for solving the fourth-order parabolic partial differential equation with variable coefficients. The results show also that the introduced method is a powerful tool for solving the fourth-order parabolic partial differential equations.

scholarly journals Positive Solutions of a Nonlinear Parabolic Partial Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Chengbo Zhai ◽  
Shunyong Li
Keyword(s):  
Differential Equation ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Monotone Operators ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Nonlinear Parabolic ◽  
Mixed Monotone Operators

We deal with the existence and uniqueness of positive solutions to a class of nonlinear parabolic partial differential equations, by using some fixed point theorems for mixed monotone operators with perturbation.

ANALYSIS OF PARABOLIC PROBLEMS ON PARTITIONED DOMAINS WITH NONLINEAR CONDITIONS AT THE INTERFACE: APPLICATION TO MASS TRANSFER THROUGH SEMI-PERMEABLE MEMBRANES

2006 ◽  
Vol 16 (04) ◽  
pp. 479-501 ◽  
Author(s):  
FRANCESCO CALABRÒ ◽  
PAOLO ZUNINO
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Parabolic Problems ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Permeable Membrane ◽  
Comparison Results ◽  
Iterative Substructuring ◽  
Neumann Type

In this work we address a problem governed by linear parabolic partial differential equations set in two adjoining domains, coupled by nonlinear interface conditions of Neumann type. In particular, we address the existence and uniqueness of strong solutions by applying the strong maximum principle, the Schauder fixed point theorem and the fundamental solutions of linear parabolic partial differential equations.In the first part of this work, we consider the properties of a linear parabolic partial differential equation set on a single domain with a nonlinear boundary condition. After having addressed the well-posedness and some comparison results for the problem on one domain, in the second part of this work we address the case of coupled problems on adjoining domains. In both cases, we complete the understanding of the behavior of the solution of the problems at hand by means of numerical simulations.The theoretical results obtained here are applied to study the behavior of a biological model for the transfer of chemicals through thin biological membranes. This model represents the dynamics of the concentration u of a chemical solution separated from the exterior by a semi-permeable membrane.The analysis of the two-domain problem that we carry out could also be used to investigate the convergence property of iterative substructuring methods applied to the approximation of multidomain problems with nonlinear coupling of Neumann type.

Numerical solution of parabolic partial differential equations using adaptive gird Haar wavelet collocation method

2016 ◽  
Vol 10 (02) ◽  
pp. 1750026 ◽  
Author(s):  
S. C. Shiralashetti ◽  
L. M. Angadi ◽  
M. H. Kantli ◽  
A. B. Deshi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Haar Wavelet ◽  
Parabolic Partial Differential Equations ◽  
Test Problems ◽  
Parabolic Pdes ◽  
Partial Differential ◽  
Wavelet Collocation Method

In this paper, we applied the adaptive grid Haar wavelet collocation method (AGHWCM) for the numerical solution of parabolic partial differential equations (PDEs). The approach of AGHWCM for the numerical solution of parabolic PDEs is mentioned, the obtained numerical results, error analysis are presented in figures and tables. This shows that, the AGHWCM gives better accuracy than the HWCM and FDM. Some of the test problems are taken for demonstrating the validity and applicability of the AGHWCM.

scholarly journals Method of Averaging for Some Parabolic Partial Differential Equations

2020 ◽  
pp. 1-4
Author(s):  
Mahmoud M. El-Borai ◽  
Hamed Kamal Awad ◽  
Randa Hamdy M. Ali
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Qualitative Analysis ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
Method Of Averaging ◽  
Exciting Field ◽  
Partial Differential ◽  
Averaging Methods

Quantitative and qualitative analysis of the Averaging methods for the parabolic partial differential equation appears as an exciting field of the investigation. In this paper, we generalize some known results due to Krol on the averaging methods and use them to solve the parabolic partial differential equation.

Reducing parabolic partial differential equations to canonical form

1994 ◽  
Vol 5 (2) ◽  
pp. 159-164 ◽  
Author(s):  
J. F. Harper
Keyword(s):  
Canonical Form ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Simple Method ◽  
Information Theoretic ◽  
Second Derivatives ◽  
Special Cases ◽  
Black Scholes ◽  
Independent Variable

A simple method of reducing a parabolic partial differential equation to canonical form if it has only one term involving second derivatives is the following: find the general solution of the first-order equation obtained by ignoring that term and then seek a solution of the original equation which is a function of one more independent variable. Special cases of the method have been given before, but are not well known. Applications occur in fluid mechanics and the theory of finance, where the Black-Scholes equation yields to the method, and where the variable corresponding to time appears to run backwards, but there is an information-theoretic reason why it should.

Parabolic Partial Differential Equations with Nonlocal Initial and Boundary Values

2015 ◽  
Vol 12 (05) ◽  
pp. 1550024 ◽  
Author(s):  
M. Turkyilmazoglu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Series Representation ◽  
Real Life ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
Algebraic Equations ◽  
Boundary Values ◽  
Partial Differential ◽  
Double Power Series

Parabolic partial differential equations possessing nonlocal initial and boundary specifications are used to model some real-life applications. This paper focuses on constructing fast and accurate analytic approximations via an easy, elegant and powerful algorithm based on a double power series representation of the solution via ordinary polynomials. Consequently, a parabolic partial differential equation is reduced to a system involving algebraic equations. Exact solutions are obtained when the solutions are themselves polynomials. Some parabolic partial differential equations are treated by the technique to judge its validity and also to measure its accuracy as compared to the existing methods.

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