An almost monotone approximation for a nonlinear two-point boundary value problem
The authors propose a new approach approximating the nonlinear two-point boundary value problem, called the almost monotone approximation. The concept of an ordered pair of supersolution and subsolution of nonlinear discrete problems is introduced. The existence and uniqueness of numerical solutions is discussed. The authors construct an almost monotone approximation of fourth order on a uniform mesh. A continuous version with the same accuracy, based on the values of the numerical solution at the mesh points given by an almost monotone approximation is presented.
nonlinear two-point boundary value problem
scientific article; zbMATH DE number 1129539
scientific article