Numerical solution of the nonlinear Dirichlet and Neumann problems based on the probabilistic approach

2004 ◽  
pp. 461-507
Author(s):  
Grigori N. Milstein ◽  
Michael V. Tretyakov
Keyword(s):  
Numerical Solution ◽  
Probabilistic Approach ◽  
Neumann Problems

scholarly journals Efficient numerical solution of Neumann problems on complicated domains

CALCOLO ◽  
2006 ◽  
Vol 43 (2) ◽  
pp. 95-120 ◽  
Author(s):  
Serge Nicaise ◽  
Stefan A. Sauter
Keyword(s):  
Numerical Solution ◽  
Neumann Problems

A probabilistic approach to quasilinear parabolic PDEs with obstacle and Neumann problems

2020 ◽  
Vol 24 ◽  
pp. 207-226
Author(s):  
Lishun Xiao ◽  
Shengjun Fan ◽  
Dejian Tian
Keyword(s):  
Probabilistic Approach ◽  
Neumann Boundary ◽  
Obstacle Problems ◽  
Parabolic Pdes ◽  
Neumann Problems ◽  
Order Coefficient ◽  
And Algebra ◽  
Convexity Constraints ◽  
Fully Coupled ◽  
Quasilinear Parabolic

In this paper, by a probabilistic approach we prove that there exists a unique viscosity solution to obstacle problems of quasilinear parabolic PDEs combined with Neumann boundary conditions and algebra equations. The existence and uniqueness for adapted solutions of fully coupled forward-backward stochastic differential equations with reflections play a crucial role. Compared with existing works, in our result the spatial variable of solutions of PDEs lives in a region without convexity constraints, the second order coefficient of PDEs depends on the gradient of the solution, and the required conditions for the coefficients are weaker.

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