Asymptotic analysis provides a set of powerful techniques for approximating solutions to differential equations, particularly in cases where exact solutions are elusive. This approach is critical when ...

Physics-informed neural networks (PINNs) represent a burgeoning paradigm in computational science, whereby deep learning frameworks are augmented with explicit physical laws to solve both forward 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 ...

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 ...

Mathematics of Computation, Vol. 59, No. 200 (Oct., 1992), pp. 403-420 (18 pages) We apply Runge-Kutta methods to linear partial differential equations of the form u t (x, t) = L (x, ∂)u(x, t) + f(x, ...

This is a preview. Log in through your library . Abstract This paper is concerned with oscillation of a certain class of second-order differential equations with a sublinear neutral term. Two ...