Abstract Waveform relaxation methods are decoupling or splitting methods for large scale ordinary differential equations. In this paper, we apply the methods directly to semi-linear parabolic partial ...

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 ...

Let the parabolic problem $c(x, t, u)u_t = a(x, t, u)u_{xx} + b(x, t, u, u_x), 0 < x < 1, 0 < t \leqq T, u(x, 0) = f(x), u(0, t) = g_0(t), u(1, t)$, be solved ...

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 ...

Off-axis paraboloid reflector is a special optical element, its main function is to focus the incident light to a certain distance from the optical axis. The working principle is based on the ...