Boundary value problems (BVPs) and spectral analysis constitute fundamental areas in the study of differential equations. These topics not only underpin theoretical advances in mathematical analysis ...

This is the first part of a two course graduate sequence in analytical methods to solve ordinary and partial differential equations of mathematical physics. Review of Advanced ODE’s including power ...

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 ...

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 ...

In this work, we find the asymptotic formulas for the sum of the negative eigenvalues smaller than −ε (ε > 0) of a self-adjoint operator L defined by the following differential expression ℓ(y) = −(p(x ...