scholarly journals High accuracy difference schemes for the system of two space nonlinear parabolic differential equations with mixed derivatives and variable coefficients

1996 ◽  
Vol 70 (1) ◽  
pp. 15-32 ◽  
Author(s):  
R.K. Mohanty ◽  
M.K. Jain
Keyword(s):  
Differential Equations ◽  
High Accuracy ◽  
Variable Coefficients ◽  
Difference Schemes ◽  
Parabolic Differential Equations ◽  
Nonlinear Parabolic ◽  
Mixed Derivatives ◽  
Accuracy Difference

scholarly journals On Some regularity properties for solutions of nonlinear parabolic differential equations

1992 ◽  
Vol 128 ◽  
pp. 49-63 ◽  
Author(s):  
Haruo Nagase
Keyword(s):  
Differential Equations ◽  
Bounded Domain ◽  
Open Interval ◽  
Function Spaces ◽  
Parabolic Differential Equations ◽  
Regularity Properties ◽  
Nonlinear Parabolic ◽  
Class C

Let G be a bounded domain in Rn with coordinates x = (x1,…,xn) and let its boundary S be of class C2. We assume that the usual function spaces Lq(G), Wl, q(G) and are known. We write the norm of Lq(G) by | |q and the adjoint number of q by q*, i.e., q* = q/(q —1).For any positive number T we denote the open interval (0,T) by I, the cylinder G X I in Rn+1 by Q and the norm of Lq(Q) by ‖ ‖q.

scholarly journals Approximate Solutions of Fisher's Type Equations with Variable Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
A. H. Bhrawy ◽  
M. A. Alghamdi
Keyword(s):  
Differential Equations ◽  
Legendre Polynomials ◽  
Nonlinear Partial Differential Equations ◽  
Approximate Solutions ◽  
High Accuracy ◽  
Variable Coefficients ◽  
Time Dependent ◽  
First Order ◽  
Spatial Derivatives ◽  
Interpolation Nodes

The spectral collocation approximations based on Legendre polynomials are used to compute the numerical solution of time-dependent Fisher’s type problems. The spatial derivatives are collocated at a Legendre-Gauss-Lobatto interpolation nodes. The proposed method has the advantage of reducing the problem to a system of ordinary differential equations in time. The four-stage A-stable implicit Runge-Kutta scheme is applied to solve the resulted system of first order in time. Numerical results show that the Legendre-Gauss-Lobatto collocation method is of high accuracy and is efficient for solving the Fisher’s type equations. Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations.

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