Nonstandard finite difference schemes for Michaelis-Menten type reaction-diffusion equations

作者：Chapwanya Michael; Lubuma Jean M S^*; Mickens Ronald E

来源：Numerical Methods for Partial Differential Equations, 2013, 29(1): 337-360.

DOI：10.1002/num.21733

• advection-reaction-diffusion equations
• exact scheme
• Lambert W function
• Michaelis-Menten equation
• nonstandard finite difference method

We compare and investigate the performance of the exact scheme of the MichaelisMenten (MM) ordinary differential equation with several new nonstandard finite difference (NSFD) schemes that we construct using Mickens%26apos; rules. Furthermore, the exact scheme of the MM equation is used to design several dynamically consistent NSFD schemes for related reaction-diffusion equations, advection-reaction equations, and advection-reaction-diffusion equations. Numerical simulations that support the theory and demonstrate computationally the power of NSFD schemes are presented.

• 出版日期2013-1