On Error Estimation and Convergence of the Difference Scheme for a Nonlinear Elliptic Equation with an Integral Boundary Condition

Regimantas Čiupaila (), Mifodijus Sapagovas, Kristina Pupalaigė and Gailė Kamilė Šaltenienė
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Regimantas Čiupaila: Department of Mathematical Modelling, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania
Mifodijus Sapagovas: Institute of Data Science and Digital Technologies, Vilnius University, Akademijos g. 4, LT-08412 Vilnius, Lithuania
Kristina Pupalaigė: Department of Applied Mathematics, Kaunas University of Technology, Studentų g. 50, LT-51368 Kaunas, Lithuania
Gailė Kamilė Šaltenienė: Department of Mathematical Modelling, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania

Mathematics, 2025, vol. 13, issue 5, 1-20

Abstract: In this paper, a two-dimensional nonlinear elliptic equation with an integral boundary condition depending on two parameters is investigated. The problem is solved using the finite difference method. The error in the solution is evaluated based on the properties of M-matrices, and herewith the convergence of the difference scheme is proved. The majorant is constructed to estimate the error of the solution of the system of difference equations.

Keywords: nonlinear elliptic equation; nonlocal boundary condition; difference eigenvalue problem; M-matrix; construction of the majorant (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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