scholarly journals A note on exponential Rosenbrock–Euler method for the finite element discretization of a semilinear parabolic partial differential equation

2018 ◽  
Vol 76 (7) ◽  
pp. 1719-1738 ◽  
Author(s):  
Jean Daniel Mukam ◽  
Antoine Tambue
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Element ◽  
Euler Method ◽  
Parabolic Partial Differential Equation ◽  
Finite Element Discretization ◽  
Partial Differential ◽  
Element Discretization ◽  
Semilinear Parabolic

scholarly journals Monte-Carlo algorithms for a forward Feynman–Kac-type representation for semilinear nonconservative partial differential equations

2018 ◽  
Vol 24 (1) ◽  
pp. 55-70 ◽  
Author(s):  
Anthony Le Cavil ◽  
Nadia Oudjane ◽  
Francesco Russo
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Monte Carlo ◽  
Numerical Experiments ◽  
Type Equation ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Type Representation ◽  
Monte Carlo Algorithms ◽  
Semilinear Parabolic

Abstract The paper is devoted to the construction of a probabilistic particle algorithm. This is related to a nonlinear forward Feynman–Kac-type equation, which represents the solution of a nonconservative semilinear parabolic partial differential equation (PDE). Illustrations of the efficiency of the algorithm are provided by numerical experiments.

scholarly journals A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation

1996 ◽  
Vol 9 (4) ◽  
pp. 399-414 ◽  
Author(s):  
Jean-François Le Gall
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Probabilistic Approach ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Brownian Snake ◽  
Nonnegative Solutions ◽  
One To One ◽  
Dimension One ◽  
Semilinear Parabolic

We use the path-valued process called the “Brownian snake” to investigate the trace at the boundary of nonnegative solutions of a semilinear parabolic partial differential equation. In particular, we characterize possible traces and in dimension one we prove that nonnegative solutions are in one-to-one correspondence with their traces at the origin. We also provide probabilistic representations for various classes of solutions.This article is dedicated to the memory of Roland L. Dobrushin.

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