Partial Differential Equations (PDEs) are mathematical equations that involve unknown multivariate functions and their partial derivatives. They are the cornerstone of modelling a vast array of ...

In this paper, we study existence and stability of solutions to a partial differential equation with 𝜓-fractional derivative. Existence results are established by means of the fixed point and upper ...

We propose a new numerical approach to solving high-dimensional partial differential equations (PDEs) that arise in the valuation of exotic derivative securities. The proposed method is extended from ...

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. 46, No. 5 (2008), pp. 2411-2442 (32 pages) This work proposes and analyzes an anisotropic sparse grid stochastic collocation method for solving partial ...

Interest rate derivatives under jump-extended short-rate models have commonly been valued using lattice methods. Unfortunately, lattice methods have pitfalls, mainly in terms of accuracy, efficiency ...