A fast implicit iterative numerical method for solving multidimensional partial differential equations

1977 ◽  
Author(s):  
W. HELLIWELL
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Partial Differential

WAVELET-BASED ADAPTIVE COLLOCATION METHOD FOR THE RESOLUTION OF NONLINEAR PDEs

2007 ◽  
Vol 05 (06) ◽  
pp. 957-973 ◽  
Author(s):  
A. KARAMI ◽  
H. R. KARIMI ◽  
B. MOSHIRI ◽  
P. JABEDAR MARALANI
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Multiresolution Analysis ◽  
Chemical Engineering ◽  
Nonlinear Pdes ◽  
Dynamic Processes ◽  
Partial Differential ◽  
Numeric Solution ◽  
Interpolating Wavelets

Theoretical modeling of dynamic processes in chemical engineering often implies the numeric solution of one or more partial differential equations. The complexity of such problems is increased when the solutions exhibit sharp moving fronts. An efficient adaptive multiresolution numerical method is described for solving systems of partial differential equations. This method is based on multiresolution analysis and interpolating wavelets, that dynamically adapts the collocation grid so that higher resolution is automatically attributed to domain regions where sharp features are present. Space derivatives were computed in an irregular grid by cubic splines method. The effectiveness of the method is demonstrated with some relevant examples in a chemical engineering context.

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