Solving the 2-D heat equations using wavelet-Galerkin method with variable time step

A wavelet-Galerkin method to solve nonhomogenous 2-D heat equations in finite rectangular domains is presented. Integrals involving nonhomogenity terms with scaling function are evaluated based on available connection coefficients. Variable time step technique is used to delay the error blow up hence obtaining better results for solutions that reach steady state.

[1]  C. Hwang,et al.  THE COMPUTATION OF WAVELET‐GALERKIN APPROXIMATION ON A BOUNDED INTERVAL , 1996 .

[2]  S. H. Behiry,et al.  A wavelet-Galerkin method for inhomogeneous diffusion equations subject to mass specification , 2002 .

[3]  Stability of Galerkin and inertial algorithms with variable time step size , 2002 .

[4]  Jacques Liandrat,et al.  DEFINITION AND ANALYSIS OF A WAVELET/FICTITIOUS DOMAIN SOLVER FOR THE 2D-HEAT EQUATION ON A GENERAL DOMAIN , 2006 .

[5]  M. K. Kaibara,et al.  Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects , 2008, Appl. Math. Comput..

[6]  Michael L. Hines,et al.  Independent Variable Time-Step Integration of Individual Neurons for Network Simulations , 2005, Neural Computation.

[7]  Mani Mehra,et al.  Fast wavelet-Taylor Galerkin method for linear and non-linear wave problems , 2007, Appl. Math. Comput..

[8]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[9]  Y. Kim,et al.  Adaptive multiscale wavelet-Galerkin analysis for plane elasticity problems and its applications to multiscale topology design optimization , 2003 .

[10]  Laura Pezza,et al.  On the Galerkin Method Based on a Particular Class of Scaling Functions , 2001, Numerical Algorithms.

[11]  Sudhakar Nair,et al.  Wavelet-Galerkin method for the free vibrations of an elastic cable carrying an attached mass , 2004 .

[12]  Jong-Shinn Wu,et al.  Parallel three-dimensional DSMC method using mesh refinement and variable time-step scheme , 2004, Comput. Phys. Commun..

[13]  Sam Qian,et al.  Wavelets and the Numerical Solution of Partial Differential Equations , 1993 .

[14]  Y. Leviatan,et al.  On the use of wavelet expansions in the method of moments (EM scattering) , 1993 .

[15]  C. Micchelli,et al.  Using the refinement equation for evaluating integrals of wavelets , 1993 .

[16]  Giuseppe Savare',et al.  A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations † , 2000 .

[17]  Kevin Amaratunga,et al.  WAVELET BASED GREEN'S FUNCTION APPROACH TO 2D PDEs , 1993 .

[18]  Mani Mehra,et al.  Time Accurate Fast Three-Step Wavelet-Galerkin Method for Partial Differential Equations , 2006, Int. J. Wavelets Multiresolution Inf. Process..

[19]  Mani Mehra,et al.  A three-step wavelet Galerkin method for parabolic and hyperbolic partial differential equations , 2006, Int. J. Comput. Math..

[20]  Yi Wang,et al.  An Implementation of Fast Wavelet Galerkin Methods for Integral Equations of the Second Kind , 2004, J. Sci. Comput..