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 ...

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...

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 ...

Convergence of a subsequence of approximate solutions arising from a full discretization is shown for a general class of quasi-linear parabolic problems. The numerical method combines the backward ...

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 ...