Existence of multiple solutions for finite difference approximations to second-order boundary value problems
This paper deals with the two-point boundary value problem \[ D^2 y_{k+1}= f(kh, y_k, Dy_k),\quad k= 1,\dots, n-1, \] \[ 0= G((y_0, y_n); (Dy_1, Dy_n)),\;Dy_k= (y_k- y_{k-1})/h,\quad h= 1/n, \] which arises as a finite difference approximation to the problem \[ y''= f(x,y,y'),\quad x\in [0,1],\quad 0= G((y(0), y(1)); (y'(0), y'(1))). \] The author extends results of \textit{R. P. Agarwal}, \textit{H. B. Thompson} and \textit{C. C. Tisdell} [On the existence of multiple solutions to boundary vaule problems for second-order ordinary differential equations (submitted for publications)] and shows that solutions of the discrete problem approximate the solutions of the continuous problem for sufficiently small grid size. Theoretical results are demostrated on certain chemical reactions in tubular reactors.
discrete two-point boundary value problems
scientific article; zbMATH DE number 1901882
scientific article