scholarly journals Monte Carlo Algorithms for the Parabolic Cauchy Problem

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 177
Author(s):  
Alexander Sipin
Keyword(s):  
Cauchy Problem ◽  
Monte Carlo ◽  
Parabolic Equation ◽  
Second Order ◽  
Unbiased Estimators ◽  
Monte Carlo Algorithms ◽  
Order Parabolic Equation ◽  
The Cauchy Problem ◽  
Smooth Coefficients

New Monte Carlo algorithms for solving the Cauchy problem for the second order parabolic equation with smooth coefficients are considered. Unbiased estimators for the solutions of this problem are constructed.

scholarly journals Nonlinear conservation laws for the Schrödinger boundary value problems of second order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ming Ren ◽  
Shiwei Yun ◽  
Zhenping Li
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Nonlinear Conservation Laws ◽  
The Cauchy Problem ◽  
Modulus Method ◽  
Semilinear Schrödinger Equation

AbstractIn this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order. As an application, we prove the global existence to the solution for the Cauchy problem of the semilinear Schrödinger equation. The results reveal that this method is effective and simple.

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