This paper analyzes a high-accuracy approximation to the $m$th-order linear ordinary differential equation $Mu = f$. At mesh points, $U$ is the estimate of $u$; and ...
An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...
This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...
Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global ...
Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...
Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...
SIAM Journal on Numerical Analysis, Vol. 50, No. 6 (2012), pp. 3351-3374 (24 pages) In this paper quasi-Monte Carlo (QMC) methods are applied to a class of elliptic partial differential equations ...
A partial differential equation (PDE) is a mathematical equation that involves multiple independent variables, an unknown function that is dependent on those variables, and partial derivatives of the ...
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