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

• Autorzy: Lucjan Sapa
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 65M06: Finite difference methods
• 35R10: Partial functional-differential equations
• 65M15: Error bounds
• 65M12: Stability and convergence of numerical methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2008
• Tom: 93
• Numer: 2
• Strony: 113-133

Daty

wydano

2008

Twórcy

autor

Lucjan Sapa

• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland

Identyfikatory

DOI

10.4064/ap93-2-2