Time-dependent Partial Differential Equations and Their Numerical Solution

2001 ◽  
Author(s):  
Heinz-Otto Kreiss ◽  
Hedwig Ulmer Busenhart
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Time Dependent ◽  
Partial Differential

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]

scholarly journals Numerical solution through mathematical modelling of unsteady MHD flow past a semi-infinite vertical moving plate with chemical reaction and radiation

2018 ◽  
Vol 40 (4) ◽  
pp. 270-281 ◽  
Author(s):  
Anupam Bhandari
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Chemical Reaction ◽  
Mhd Flow ◽  
Time Dependent ◽  
Physical Parameters ◽  
Concentration Profiles ◽  
Partial Differential

Abstract In the present manuscript, unsteady magnetohydrodynamic (MHD) flow over a moving porous semi-infinite vertical plate with time-dependent suction has been studied in the presence of chemical reaction and radiation parameters. Time-dependent partial differential equations in the dimensionless form are solved numerically through mathematical modelling in COMSOL Multiphysics. The results are obtained for velocity, temperature and concentration profiles at different times. Steady state results are also presented for different values of physical parameters. The parameters involved in the problem are useful to change the characteristics of velocity, heat transfer and concentration profiles. The numerical solution of partial differential equations involved in the problem is obtained without sacrificing the relevant physical phenomena.

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