Raza, Nauman; Sial, Sultan; Siddiqi, S. Approximating time evolution related to Ginzburg-Landau functionals via Sobolev gradient methods in a finite-element setting. (English) Zbl 1181.65124 J. Comput. Phys. 229, No. 5, 1621-1625 (2010). MSC: 65M60 PDFBibTeX XMLCite \textit{N. Raza} et al., J. Comput. Phys. 229, No. 5, 1621--1625 (2010; Zbl 1181.65124) Full Text: DOI
Raza, Nauman; Sial, Sultan; Siddiqi, Shahid S. Simulation study of propagation of pulses in optical fiber communication systems using Sobolev gradient and split-step Fourier methods. (English) Zbl 1264.78043 Int. J. Comput. Methods 6, No. 1, 119-130 (2009). MSC: 78M25 78M20 78A10 78A60 PDFBibTeX XMLCite \textit{N. Raza} et al., Int. J. Comput. Methods 6, No. 1, 119--130 (2009; Zbl 1264.78043) Full Text: DOI
Raza, Nauman; Sial, Sultan; Siddiqi, Shahid S.; Lookman, Turab Energy minimization related to the nonlinear Schrödinger equation. (English) Zbl 1161.65339 J. Comput. Phys. 228, No. 7, 2572-2577 (2009). MSC: 65K10 49M15 81Q05 PDFBibTeX XMLCite \textit{N. Raza} et al., J. Comput. Phys. 228, No. 7, 2572--2577 (2009; Zbl 1161.65339) Full Text: DOI
Raza, Nauman; Sial, Sultan; Siddiqi, Shahid S. Sobolev gradient approach for the time evolution related to energy minimization of Ginzburg-Landau functionals. (English) Zbl 1166.65348 J. Comput. Phys. 228, No. 7, 2566-2571 (2009). MSC: 65K10 49M25 82C80 PDFBibTeX XMLCite \textit{N. Raza} et al., J. Comput. Phys. 228, No. 7, 2566--2571 (2009; Zbl 1166.65348) Full Text: DOI