Explicit finite difference schemes adapted to advection–reaction equations

References

• McCartin , B. J. 2006 . The exponential method of angled derivatives . Applied Mathematics and Computation , 177 : 665 – 685 .
   Google Scholar
• Rhee , H. , Aris , R. and Amundson , N. R. 2001 . First Order Partial Differential Equations, Theory and Application of Single Equations , Vol. I , New York : Dover .
   Google Scholar
• Finlayson , B. A. 1992 . Numerical Methods for Problems with Moving Fronts , Seattle, WA : Ravenna Park .
   Google Scholar
• McCartin , B. J. and Young , P. D. 2005 . “ Numerical investigation of the validity of the quasi-static approximation in the modelling of catalytic converters ” . In Mathematics and Industry , Edited by: Freguson , D. and Peters , T. Philadelphia, PA : SIAM .
   Google Scholar
• Martín-Vaquero , J. and Vigo-Aguiar , J. 2006 . Exponential fitting BDF algorithms: explicit and implicit 0-stable methods . Journal of Computational and Applied Mathematics , 192 : 100 – 113 .
   Google Scholar
• Vigo-Aguiar , J. and Ferrándiz , J. M. 1998 . A general procedure for the adaptation of multistep algorithms to the integration of oscillatory problems . SIAM Journal on Numerical Analysis , 35 : 1684 – 1708 .
   Google Scholar
• Vigo-Aguiar , J. and Simos , T. E. 2002 . Family of twelve steps exponential fitting symmetric multistep methods for the numerical solution of the Schrödinger equation . Journal of Mathematical Chemistry , 32 : 257 – 270 .
   Web of Science ®Google Scholar
• Vigo-Aguiar , J. , Martín-Vaquero , J. and Criado , R. 2005 . On the stability of exponential fitting BDF algorithms . Journal of Computational and Applied Mathematics , 175 : 183 – 194 .
   Google Scholar
• Vigo-Aguiar , J. , Martín-Vaquero , J. and Wade , B. 2007 . Adapted BDF algorithms applied to parabolic problems . Numerical Methods for Partial Differential Equations , 23 : 350 – 365 .
   Google Scholar
• Martín-Vaquero , J. and Vigo-Aguiar , J. 2007 . Adapted BDF algorithms: higher-order methods and their stability . Journal of Scientific Computing , 32 : 287 – 313 .
   Google Scholar
• Martín-Vaquero , J. 2006 . “ Métodos exponential fitting y adaptados para problemas stiff ” . University Rey Juan Carlos (in Spanish) . PhD
   Google Scholar
• Strikwerda , J. C. 2004 . Finite Difference Schemes and Partial Differential Equations , 2 , Philadelphia, PA : SIAM .
   Google Scholar
• Ahmad , I. and Berzins , M. 2001 . MOL solvers for hyperbolic PDEs with source terms . Mathematics and Computers in Simulation , 56 : 115 – 125 .
   Google Scholar
• Ahmad , R. R. and Yaacob , N. 2005 . Third-order composite Runge—Kutta method for stiff problems . International Journal of Computer Mathematics , 82 : 1221 – 1226 .
   Web of Science ®Google Scholar
• Kumar , R. B.V. and Mehra , M. 2006 . A three-step wavelet Galerkin method for parabolic and hyperbolic partial differential equations . International Journal of Computer Mathematics , 83 : 143 – 157 .
   Web of Science ®Google Scholar
• Saucez , P. , Schiesser , W. E. and Vande Wouwer , A. 2001 . Upwinding in the method of lines . Mathematics and Computers in Simulation , 56 : 171 – 185 .
   Google Scholar
• Sethian , J. A. 1999 . Fast marching methods . SIAM Review , 41 : 199 – 235 .
   Web of Science ®Google Scholar
• Wang , T. 2005 . New characteristic difference method with adaptive mesh for one-dimensional unsteady convection-dominated diffusion equations . International Journal of Computer Mathematics , 82 : 1247 – 1260 .
   Web of Science ®Google Scholar
• Leveque , R. J. and Yee , H. C. 1990 . A study of numerical methods for hyperbolic conservation laws with stiff source terms . Journal of Computational Physics , 86 : 187 – 210 .
   Web of Science ®Google Scholar