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 ...

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 ...

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 propose to use stratified approximations based on the gamma and lognormal distributions for the pricing of options on average, such as Asian options and bond prices in the Dothan model. We show ...

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 ...