Numerical simulation of blowup in nonlocal reaction-diffusion equations using a moving mesh method

• Autores: Jingtang Ma, Yingjun Jiang, Kaili Xiang
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 230, Nº 1, 2009, págs. 8-21
• Idioma: inglés
• DOI: 10.1016/j.cam.2008.10.063
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we implement the moving mesh PDE method for simulating the blowup in reaction�diffusion equations with temporal and spacial nonlinear nonlocal terms. By a time-dependent transformation, the physical equation is written into a Lagrangian form with respect to the computational variables. The time-dependent transformation function satisfies a parabolic partial differential equation � usually called moving mesh PDE (MMPDE). The transformed physical equation and MMPDE are solved alternately by central finite difference method combined with a backward time-stepping scheme. The integration time steps are chosen to be adaptive to the blowup solution by employing a simple and efficient approach. The monitor function in MMPDEs plays a key role in the performance of the moving mesh PDE method. The dominance of equidistribution is utilized to select the monitor functions and a formal analysis is performed to check the principle. A variety of numerical examples show that the blowup profiles can be expressed correctly in the computational coordinates and the blowup rates are determined by the tests.