PARALLEL NUMERICAL SOLUTION PROCESS OF A TWO DIMENSIONAL TIME DEPENDENT NONLINEAR PARTIAL DIFFERENTIAL EQUATION

1995 ◽  
Author(s):  
I. MARTIN ◽  
F. TIRADO ◽  
L. VAZQUEZ
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solution ◽  
Nonlinear Partial Differential Equation ◽  
Solution Process ◽  
Time Dependent ◽  
Two Dimensional ◽  
Partial Differential

scholarly journals On the Properties of Two-Dimensional Normalized Boubaker Polynomials

2020 ◽  
Vol 55 (3) ◽  
Author(s):  
Mohammed Abdelhadi Sarhan ◽  
Suha Shihab ◽  
Mohammed Rasheed
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solution ◽  
Suggested Method ◽  
Operational Matrices ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Boubaker Polynomials ◽  
Derived Properties

The aim of the present work deals with newly defined two-variable polynomials for normalized Boubaker . The operational matrices of derivatives with respect to the two variables are presented at first with explicit expression. Then, a normalized Boubaker polynomial approximation for the numerical solution of a class of partial differential equations is proposed, depending on a truncated, normalized Boubaker function series in the equation together with the operational matrices in the proposed partial differential equation. The original partial differential equation is reduced under consideration of a system of simply solvable algebraic equations. Due to the interesting derived properties of normalized Boubaker polynomials in two variables, the suggested method can achieve good results with few complexities. Using operational matrices of derivatives, one can save computation and more memory. Two-dimensional examples are listed to show the satisfactory level of the suggested method.

Numerical Solution of Fractional Partial Differential Equation of Parabolic Type With Dirichlet Boundary Conditions Using Two-Dimensional Legendre Wavelets Method

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
S. Saha Ray ◽  
A. K. Gupta
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solution ◽  
Parabolic Type ◽  
Order Partial Differential Equation ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Partial Differential ◽  
Wavelet Method ◽  
Fractional Pde

In this paper, the numerical solution for the fractional order partial differential equation (PDE) of parabolic type has been presented using two dimensional (2D) Legendre wavelets method. 2D Haar wavelets method is also applied to compute the numerical solution of nonlinear time-fractional PDE. The approximate solutions of nonlinear fractional PDE thus obtained by Haar wavelet method and Legendre wavelet method are compared with the exact solution obtained by using homotopy perturbation method (HPM). The present scheme is simple, effective, and expedient for obtaining numerical solution of the fractional PDE.

scholarly journals Healing capillary films

2018 ◽  
Vol 838 ◽  
pp. 404-434 ◽  
Author(s):  
Zhong Zheng ◽  
Marco A. Fontelos ◽  
Sangwoo Shin ◽  
Michael C. Dallaston ◽  
Dmitri Tseluiko ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Time ◽  
Finite Thickness ◽  
Nonlinear Partial Differential Equation ◽  
Time Dependent ◽  
Scaling Exponent ◽  
Partial Differential ◽  
Self Similar ◽  
Similar Solutions

Consider the dynamics of a healing film driven by surface tension, that is, the inward spreading process of a liquid film to fill a hole. The film is modelled using the lubrication (or thin-film) approximation, which results in a fourth-order nonlinear partial differential equation. We obtain a self-similar solution describing the early-time relaxation of an initial step-function condition and a family of self-similar solutions governing the finite-time healing. The similarity exponent of this family of solutions is not determined purely from scaling arguments; instead, the scaling exponent is a function of the finite thickness of the prewetting film, which we determine numerically. Thus, the solutions that govern the finite-time healing are self-similar solutions of the second kind. Laboratory experiments and time-dependent computations of the partial differential equation are also performed. We compare the self-similar profiles and exponents, obtained by matching the estimated prewetting film thickness, with both measurements in experiments and time-dependent computations near the healing time, and we observe good agreement in each case.

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