scholarly journals 7. On The Notion Of Boundary Conditions In Comparison Principles For Viscosity Solutions

2018 ◽  
pp. 143-154
Keyword(s):  
Boundary Conditions ◽  
Viscosity Solutions ◽  
Comparison Principles

scholarly journals Coupling Lévy measures and comparison principles for viscosity solutions

2019 ◽  
Vol 372 (10) ◽  
pp. 7327-7370
Author(s):  
Nestor Guillen ◽  
Chenchen Mou ◽  
Andrzej Świȩch
Keyword(s):  
Viscosity Solutions ◽  
Comparison Principles ◽  
Lévy Measures

NUMERICAL APPROXIMATION OF VISCOSITY SOLUTIONS OF FIRST-ORDER HAMILTON-JACOBI EQUATIONS WITH NEUMANN TYPE BOUNDARY CONDITIONS

1992 ◽  
Vol 02 (03) ◽  
pp. 357-374 ◽  
Author(s):  
ELISABETH ROUY
Keyword(s):  
Boundary Conditions ◽  
Viscosity Solutions ◽  
Numerical Approximation ◽  
Time Discretization ◽  
Finite Difference Schemes ◽  
First Order ◽  
The Cauchy Problem ◽  
Neumann Type ◽  
Type Boundary ◽  
Jacobi Equations

We present a general result concerning numerical approximations, obtained by finite difference schemes, of viscosity solutions to the Cauchy problem for first-order Hamilton-Jacobi equations with Neumann type boundary conditions. It states that if Δt is the time-discretization , then the error estimate between the approximation and the solution is of the order [Formula: see text] under certain assumptions of monotonicity and consistency on the numerical scheme.

scholarly journals Convergence of solutions for functional integro-differential equations with nonlinear boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Peiguang Wang ◽  
Yameng Wang ◽  
Cuimei Jiang ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Unique Solution ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Quasilinearization Method ◽  
Comparison Principles ◽  
Monotone Iterative ◽  
Convergence Of Solutions

AbstractThis paper is concerned with the convergence of solutions for a class of functional integro-differential equations with nonlinear boundary conditions. New comparison principles are obtained. By using the comparison principles and quasilinearization method, we present two monotone iterative sequences uniformly and monotonically converging to the unique solution with rate of order 2. Meanwhile, an example is given to demonstrate applications of the result reported.

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