Efficient numerical solution of Fisher's equation by using B-spline method

References

• Ablowitz, M. , and Zepetella, A. , 1979. Explicit solution of Fisher's equation for a special wave speed , Bull. Math. Biol. 41 (1979), pp. 835–840.
   Web of Science ®Google Scholar
• Al-Khaled, K. , 2001. Numerical study of Fisher's reaction-diffusion equation by the sinc collocation method , J. Comput. Appl. Math. 137 (2001), pp. 245–255.
   Web of Science ®Google Scholar
• Caglar, H. N. , Caglar, S. H. , and Twizell, E. H. , 1999. The numerical solution of third-order boundary-value problems with fourth-degree B-spline functions , Int. J. Comput. Math. 71 (1999), pp. 373–381.
   Web of Science ®Google Scholar
• Caglar, H. N. , Caglar, S. H. , and Twizell, E. H. , 1999. The numerical solution of fifth-order boundary-value problems with sixth-degree B-spline functions , Appl. Math. Lett. 12 (1999), pp. 25–30.
   Web of Science ®Google Scholar
• Canosa, J. , 1973. On a nonlinear diffusion equation describing population growth , IBM J. Res. Develop. 17 (1973), pp. 307–313.
   Web of Science ®Google Scholar
• Cattani, C. , and Kudreyko, A. , 2008. Mutiscale Analysis of the Fisher Equation . Vol. 5072. Berlin/Heidelberg: Springer-Verlag; 2008. pp. 1171–1180, ICCSA 2008, Part I, Lecture Notes in Computer Science.
   Google Scholar
• El-Azab, M. S. , 2007. An approximation scheme for a nonlinear diffusion Fisher's equation , Appl. Math. Comput. 186 (2007), pp. 579–588.
   Web of Science ®Google Scholar
• Fisher, R. A. , 1937. The wave of advance of advantageous genes , Ann. Eugenics 7 (1937), pp. 355–369.
   Google Scholar
• Gazdag, J. , and Canosa, J. , 1974. Numerical solution of Fisher's equation , J. Appl. Probab. 11 (1974), pp. 445–457.
   Web of Science ®Google Scholar
• Kadalbajoo, M. K. , Gupta, V. , and Awasthi, A. , 2008. A uniformly convergent B-spline collocation method on a non uniform mesh for singularly perturbed one-dimensional time-dependent linear convection–diffusion problem , J. Comput. Appl. Math. 220 (2008), pp. 271–289.
   Web of Science ®Google Scholar
• Li, S. , Petzold, L. , and Ren, Y. , 1998. Stability of moving mesh systems of partial differential equations , SIAM J. Sci. Comput. 20 (1998), pp. 719–738.
   Web of Science ®Google Scholar
• Mickens, R. E. , 1994. A best finite-difference scheme for Fisher's equation , Numer. Meth. Part. Diff. Eqns. 10 (1994), pp. 581–585.
   Google Scholar
• Mittal, R. C. , and Kumar, S. , 2006. Numerical study of Fisher's equation by wavelet Galerkin method , Int. J. Comput. Math. 83 (2006), pp. 287–298.
   Web of Science ®Google Scholar
• Olmos, D. , and Shizgal, B. D. , 2006. A pseudospectral method of solution of Fisher's equation , J. Comput. Appl. Math. 193 (2006), pp. 219–242.
   Web of Science ®Google Scholar
• Parekh, N. , and Puri, S. , 1990. A new numerical scheme for the Fisher's equation , J. Phys. A 23 (1990), pp. L1085–L1091.
   Google Scholar
• Qiu, Y. , and Sloan, D. M. , 1998. Numerical solution of Fisher's equation using a moving mesh method , J. Comput. Phys. 146 (1998), pp. 726–746.
   Web of Science ®Google Scholar
• Sahin, A. , Dag, I. , and Saka, B. , 2008. A B-spline algorithm for the numerical solution of Fisher's equation , Kybernetes 37 (2008), pp. 326–342, Emerald Group Publishing Limited 0368 492X.
   Web of Science ®Google Scholar
• Sherratt, J. , 1998. On the transition from initial data traveling waves in the Fisher–KPP equation , Dyn. Stab. Syst. 13 (2) (1998), pp. 167–174.
   Google Scholar
• Tang, S. , and Weber, R. O. , 1991. Numerical study of Fisher's equation by a Petrov–Galerkin finite element method , J. Aus. Math. Soc. Sci. B 33 (1991), pp. 27–38.
   Google Scholar
• Twizell, E. H. , Wang, Y. , and Price, W. G. , 1990. Chaos free numerical solutions of reaction–diffusion equations , Proc. R. Soc. London Sci. A. 430 (1990), pp. 541–576.
   Web of Science ®Google Scholar
• Wazwaz, A. M. , 2007. The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations , Appl. Math. Comput. 188 (2007), pp. 1467–1475.
   Web of Science ®Google Scholar
• Wazwaz, A. M. , and Gorguis, A. , 2004. An analytic study of Fisher's equation by using Adomian decomposition method , Appl. Math. Comput. 154 (2004), pp. 609–620.
   Web of Science ®Google Scholar
• Wen-Shan, D. , Hong-Juan, Y. , and Yu-Ren, S. , 2006. An exact solution of Fisher equation and its stability , Chinese Phys. 15 (7) (2006), pp. 1414–1417.
   Google Scholar
• Zhao, S. , and Wei, G. W. , 2003. Comparison of the discrete singular convolution and three other numerical schemes for solving Fisher's equation , SIAM Comput. 25 (1) (2003), pp. 127–147.
   Web of Science ®Google Scholar