scholarly journals RBFs Meshless Method of Lines for the Numerical Solution of Time-Dependent Nonlinear Coupled Partial Differential Equations

2011 ◽  
Vol 02 (04) ◽  
pp. 414-423 ◽  
Author(s):  
Sirajul Haq ◽  
Arshad Hussain ◽  
Marjan Uddin
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Meshless Method ◽  
Method Of Lines ◽  
Time Dependent ◽  
Partial Differential ◽  
Coupled Partial Differential Equations ◽  
Meshless Method Of Lines

scholarly journals Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Jafar Biazar ◽  
Mohammad Hosami
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Meshless Method ◽  
Time Dependent ◽  
Arc Length ◽  
Adaptive Meshes ◽  
Partial Differential ◽  
Monitor Function ◽  
Ill Conditioning ◽  
Set Of Points

Meshless method of line is a powerful device to solve time-dependent partial differential equations. In integrating step, choosing a suitable set of points, such as adaptive nodes in spatial domain, can be useful, although in some cases this can cause ill-conditioning. In this paper, to produce smooth adaptive points in each step of the method, two constraints are enforced in Equidistribution algorithm. These constraints lead to two different meshes known as quasi-uniform and locally bounded meshes. These avoid the ill-conditioning in applying radial basis functions. Moreover, to generate more smooth adaptive meshes another modification is investigated, such as using modified arc-length monitor function in Equidistribution algorithm. Influence of them in growing the accuracy is investigated by some numerical examples. The results of consideration of two constraints are compared with each other and also with uniform meshes.

Some recent methods for the numerical solution of time-dependent partial differential equations

1971 ◽  
Vol 323 (1553) ◽  
pp. 219-235 ◽  
Keyword(s):  
Partial Differential Equations ◽  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Solution ◽  
Time Dependent ◽  
Partial Differential

Numerical methods for the solution of time-dependent partial differential equations are classified under three headings and members of each class are considered in some detail. A survey of the relative merits of the hopscotch class of algorithms and of methods of Galerkin type is given with particular reference to the needs of the user. Some suggestions for possible developments in this field are included in the hope that they may lead to powerful schemes for the solution of partial differential equations.

scholarly journals Derivation of boundary conditions for the artificial boundaries associated with the solution of certain time dependent problems by Lax–Wendroff type difference schemes

1982 ◽  
Vol 25 (1) ◽  
pp. 1-18 ◽  
Author(s):  
John C. Wilson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Time Dependent ◽  
Finite Region ◽  
Partial Differential ◽  
Artificial Boundaries ◽  
Fixed Boundaries ◽  
Time Dependent Problems

Many problems involving the solution of partial differential equations require the solution over a finite region with fixed boundaries on which conditions are prescribed. It is a well known fact that the numerical solution of many such problems requires additional conditions on these boundaries and these conditions must be chosen to ensure stability. This problem has been considered by, amongst others, Kreiss [11, 12, 13], Osher [16, 17], Gustafsson et al. [9] Gottlieb and Tarkel [7] and Burns [1]

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