Using Newton basis functions for solving diffusion equation with nonlocal boundary condition (Q1742866)

The authors are concerned with numerical approximation of diffusion equations featuring nonlocal boundary conditions. A meshless method based on spatial trial spaces spanned by the Newton basis functions is employed. The time-dependent differential equation is discretized in space by the collocation method based on Newton basis functions as trial functions and it is converted to a system of ordinary differential equations in time. Stability of the scheme is also discussed. Numerical experiments are included in order to illustrate the theoretical findings.