Rothe's method for parabolic initial boundary value problems, also known as the horizontal line method, consists of a time discretization by finite differences and leads to a sequence of boundary ...

In this paper, the time-fractional heat equation with the Caputo derivative of order α where 0 < α ≤ 1 is considered. The parametric Crank-Nicholson type method for direct problems is used. But for ...

Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

Accurate prediction of radiative heating during rocket descent poses a fundamental challenge for reusable launch vehicle design. Traditional methods struggle to balance computational cost with ...