Invariant variational principles and conservation laws for some nonlinear partial differential equations with variable coefficients part II

2003 ◽  
Vol 15 (1) ◽  
pp. 1-13 ◽  
Author(s):  
A.H. Khater ◽  
M.H.M. Moussa ◽  
S.F. Abdul-Aziz
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Variational Principles ◽  
Nonlinear Partial Differential Equations ◽  
Variable Coefficients ◽  
Partial Differential

Extended Conservation Laws of Some Nonlinear Partial Differential Equations

2010 ◽  
Vol 53 (4) ◽  
pp. 693-697 ◽  
Author(s):  
Song Zhao-Hui ◽  
Mei Jian-Qin ◽  
Zhang Hong-Qing
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential

scholarly journals Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 164-169
Author(s):  
Maysaa Mohamed Al Qurashi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Nonlinear Partial Differential Equations ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Systems Of Pdes ◽  
First Time ◽  
Conservation Theorem

AbstractIn this paper, we examine conservation laws (Cls) with conformable derivative for certain nonlinear partial differential equations (PDEs). The new conservation theorem is used to the construction of nonlocal Cls for the governing systems of equation. It is worth noting that this paper introduces for the first time, to our knowledge, the analysis for Cls to systems of PDEs with a conformable derivative.

scholarly journals Approximate Solutions of Nonlinear Partial Differential Equations Using B-Polynomial Bases

2021 ◽  
Vol 5 (3) ◽  
pp. 106
Author(s):  
Muhammad Bhatti ◽  
Md. Rahman ◽  
Nicholas Dimakis
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Matrix Equation ◽  
Initial Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Initial Guess ◽  
Partial Differential

A multivariable technique has been incorporated for guesstimating solutions of Nonlinear Partial Differential Equations (NPDE) using bases set of B-Polynomials (B-polys). To approximate the anticipated solution of the NPD equation, a linear product of variable coefficients ai(t) and B-polys Bi(x) has been employed. Additionally, the variable quantities in the anticipated solution are determined using the Galerkin method for minimizing errors. Before the minimization process is to take place, the NPDE is converted into an operational matrix equation which, when inverted, yields values of the undefined coefficients in the expected solution. The nonlinear terms of the NPDE are combined in the operational matrix equation using the initial guess and iterated until converged values of coefficients are obtained. A valid converged solution of NPDE is established when an appropriate degree of B-poly basis is employed, and the initial conditions are imposed on the operational matrix before the inverse is invoked. However, the accuracy of the solution depends on the number of B-polys of a certain degree expressed in multidimensional variables. Four examples of NPDE have been worked out to show the efficacy and accuracy of the two-dimensional B-poly technique. The estimated solutions of the examples are compared with the known exact solutions and an excellent agreement is found between them. In calculating the solutions of the NPD equations, the currently employed technique provides a higher-order precision compared to the finite difference method. The present technique could be readily extended to solving complex partial differential equations in multivariable problems.

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