2 research outputs found
Efficient Numerical Scheme for Solving (1+1), (2+1)-dimensional and Coupled Burgers Equation
A numerical scheme based on backward differentiation formula (BDF) and
generalized differential quadrature method (GDQM) has been developed. The
proposed scheme has been employed to investigate three cases of Burgers
equation, one-dimensional, two-dimensional and two-dimensional coupled models.
The results showed an effectiveness accuracy in absolute error and error norm
Optimizing time-spectral solution of initial-value problems
Time-spectral solution of ordinary and partial differential equations is
often regarded as an inefficient approach. The associated extension of the time
domain, as compared to finite difference methods, is believed to result in
uncomfortably many numerical operations and high memory requirements. It is
shown in this work that performance is substantially enhanced by the
introduction of algorithms for temporal and spatial subdomains in combination
with sparse matrix methods. The accuracy and efficiency of the recently
developed time spectral, generalized weighted residual method (GWRM) is
compared to that of the explicit Lax-Wendroff method and the implicit
Crank-Nicolson method. Three initial-value PDEs are employed as model problems;
the 1D Burger equation, a forced 1D wave equation and a coupled system of 14
linearized ideal magnetohydrodynamic (MHD) equations. It is found that the GWRM
is more efficient than the time-stepping methods at high accuracies. For
time-averaged solution of the two-time-scales, forced wave equation GWRM
performance exceeds the finite difference methods by an order of magnitude both
in terms of CPU time and memory requirement. Favourable scaling of CPU time and
memory usage with the number of temporal and spatial subdomains is demonstrated
for the MHD equations.Comment: 17 pages, 3 figure