Shifted Jacobi spectral-Galerkin method for solving hyperbolic partial differential equations

2019 ◽  
Vol 78 (3) ◽  
pp. 889-904 ◽  
Author(s):  
E.H. Doha ◽  
R.M. Hafez ◽  
Y.H. Youssri
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Spectral Galerkin Method

scholarly journals A WAVELET-TAYLOR GALERKIN METHOD FOR PARABOLIC AND HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS

2005 ◽  
Vol 02 (01) ◽  
pp. 75-97 ◽  
Author(s):  
B. V. RATHISH KUMAR ◽  
MANI MEHRA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Linear Differential Operator ◽  
Nonlinear Function ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Taylor Series Expansions ◽  
Time Marching ◽  
Linear Differential

In this study a set of new space and time accurate numerical methods based on different time marching schemes such as Euler, leap-frog and Crank-Nicolson for partial differential equations of the form [Formula: see text], where ℒ is linear differential operator and [Formula: see text] is a nonlinear function, are proposed. To produce accurate temporal differencing, the method employs forward/backward time Taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation. This yields a generalized time discretized scheme which is approximated in space by Galerkin method. The compactly supported orthogonal wavelet bases developed by Daubechies are used in Galerkin scheme. This new wavelet-Taylor Galerkin approach is successively applied to heat equation, convection equation and inviscid Burgers' equation.

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