A variational-difference method for solving two-dimensional linear parabolic equations

1977 ◽  
Vol 17 (1) ◽  
pp. 101-111 ◽  
Author(s):  
Yu.R. Akopyan ◽  
L.A. Oganesyan
Keyword(s):  
Difference Method ◽  
Parabolic Equations ◽  
Two Dimensional ◽  
Linear Parabolic Equations ◽  
Variational Difference Method

scholarly journals Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations

2005 ◽  
Vol 2005 (4) ◽  
pp. 523-536
Author(s):  
Yubin Yan
Keyword(s):  
Difference Method ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Approximation Scheme ◽  
Time Derivative ◽  
Nonsmooth Data ◽  
Smoothing Property ◽  
Linear Parabolic Equations ◽  
Linear Parabolic Problem ◽  
Data Error

A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for the approximation of time derivative has been obtained.

scholarly journals Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order

2018 ◽  
Vol 3 (1) ◽  
pp. 255-264 ◽  
Author(s):  
F. Talay Akyildiz ◽  
K. Vajravelu
Keyword(s):  
Spectral Method ◽  
Parabolic Equations ◽  
Splitting Method ◽  
Higher Order ◽  
Two Dimensional ◽  
Order Accuracy ◽  
Special Cases ◽  
Linear Parabolic Equations ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral

AbstractIn this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations. Galerkin-Chebyshev pseudo spectral method is used for discretization of the spatial derivatives, and implicit Euler method is used for temporal discretization. In addition, we use this novel method to solve the well-known semi-linear Poisson-Boltzmann (PB) model equation and obtain solutions with higher-order accuracy. Furthermore, we compare the results obtained by our method for the semi-linear parabolic equation with the available analytical results in the literature for some special cases, and found excellent agreement. Furthermore, our new technique is also applicable for three-dimensional problems.

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