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

• Autorzy: Lucjan Sapa
• Języki publikacji: EN

Abstrakty

EN

Classical solutions of nonlinear second-order partial differential functional equations of parabolic type with Neumann’s condition are approximated in the paper by solutions of associated explicit difference functional equations. The functional dependence is of the Volterra type. Nonlinear estimates of the generalized Perron type for given functions are assumed. The convergence and stability results are proved with the use of the comparison technique. These theorems in particular cover quasi-linear equations, but such equations are also treated separately. The known results on similar difference methods can be obtained as particular cases of our simple result.

Słowa kluczowe

EN

parabolic differential functional equations; difference methods; nonlinear estimates of the generalized Perron type

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2009
• Tom: 49
• Numer: 1

Daty

wydano

2009

online

2017-12-19

Twórcy

autor

Lucjan Sapa

Identyfikatory

DOI

10.14708/cm.v49i1.5281