The first boundary value problem for second-order quasilinear parabolic equations with principal part in divergence form

1991 ◽  
pp. 7-30
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Principal Part ◽  
Boundary Value ◽  
Divergence Form ◽  
Second Order ◽  
Quasilinear Parabolic Equations ◽  
Quasilinear Parabolic

scholarly journals Iterative solution of quasilinear parabolic equations by parabolic equations with constant coefficients

1982 ◽  
Vol 24 (2) ◽  
pp. 203-222
Author(s):  
John E. Lavery
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Quasilinear Parabolic Equations ◽  
Constant Coefficients ◽  
Initial Boundary Value ◽  
Quasilinear Parabolic

AbstractA method for solving quasilinear parabolic equations of the typesthat differs radically from previously known methods is proposed. For each initial-boundary-value problem of one of these types that has boundary conditions of the first kind (second kind), a conjugate initial-boundary-value problem of the other type that has boundary conditions of the second kind (first kind) is defined. Based on the relations connecting the solutions of a pair of conjugate problems, a series of parabolic equations with constant coefficients that do not change step to step is constructed. The method proposed consists in calculating the solutions of the equations of this series. It is shown to have linear convergence. Results of a series of numerical experiments in a finite-difference setting show that one particular implementation of the proposed method has a smaller domain of convergence than Newton's method but that it sometimes converges faster within that domain.

Sign in / Sign up

Export Citation Format

Share Document