A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Dirichlet's condition

作者：Sapa Lucjan^*

来源：Annales Polonici Mathematici, 2008, 93(2): 113-133.

DOI：10.4064/ap93-2-2

• nonlinear and quasi-linear differential functional equations of parabolic type
• finite difference methods
• stability and convergence
• nonlinear estimates of the generalized Perron type

We deal with a finite difference method for a wide class of nonlinear, in particular strongly nonlinear or quasi-linear, second-order partial differential functional equations of parabolic type with Dirichlet's condition. The functional dependence is of the Volterra type and the right-hand sides of the equations satisfy nonlinear estimates of the generalized Perron type with respect to the functional variable. Under the assumptions adopted, quasi-linear equations are a special case of nonlinear equations. Quasi-linear equations are also treated separately. It is proved that our numerical methods are consistent, convergent and stable. Error estimates are given. The proofs are based on the comparison technique. Examples of physical applications and numerical experiments are presented.

• 出版日期2008