Dual Schur Method in Time for Nonlinear ODE

2016 ◽  
pp. 577-585
Author(s):  
P. Linel ◽  
D. Tromeur-Dervout
Keyword(s):  
Nonlinear Ode

A Computational Tool for the Reduction of Nonlinear ODE Systems Possessing Multiple Scales

2005 ◽  
Vol 4 (3) ◽  
pp. 732-759 ◽  
Author(s):  
Robert Clewley ◽  
Horacio G. Rotstein ◽  
Nancy Kopell
Keyword(s):  
Multiple Scales ◽  
Computational Tool ◽  
Nonlinear Ode ◽  
Ode Systems

scholarly journals Numerical Techniques for Unsteady Nonlinear Burgers Equation Based on Backward Differentiation Formulas

2018 ◽  
Vol 7 (3) ◽  
pp. 171-181 ◽  
Author(s):  
Vijitha Mukundan ◽  
Ashish Awasthi
Keyword(s):  
Numerical Solutions ◽  
Burgers Equation ◽  
Numerical Technique ◽  
System Stability ◽  
Test Problems ◽  
Numerical Techniques ◽  
Ode System ◽  
Backward Differentiation Formulas ◽  
Nonlinear Ode ◽  
Differentiation Formulas

AbstractWe introduce new numerical techniques for solving nonlinear unsteady Burgers equation. The numerical technique involves discretization of all variables except the time variable which converts nonlinear PDE into nonlinear ODE system. Stability of the nonlinear system is verified using Lyapunov’s stability criteria. Implicit stiff solvers backward differentiation formula of order one, two and three are used to solve the nonlinear ODE system. Four test problems are included to show the applicability of introduced numerical techniques. Numerical solutions so obtained are compared with solutions of existing schemes in literature. The proposed numerical schemes are found to be simple, accurate, fast, practical and superior to some existing methods.

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