Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical approximation of these equations ...

Approximation theory and asymptotic methods form a foundational framework that bridges classical ideas with modern numerical analysis, enabling researchers to obtain practical, near‐optimal solutions ...

We consider the numerical approximation of a semilinear fractional order evolution equation involving a Caputo derivative in time of order α ϵ (0,1). Assuming a Lipschitz continuous nonlinear source ...

In their 2001 paper, Longstaff and Schwartz suggested a method for American option pricing using simulation and regression, and since then this method has rapidly gained importance. However, the idea ...