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

Author

Listed:
  • 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
    Department of Mechanical and Civil Engineering, Kaunas University of Applied Engineering Sciences, Tvirtovės al. 35, LT-50155 Kaunas, Lithuania)

  • Gailė Kamilė Šaltenienė

    (Department of Mathematical Modelling, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania)

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.

Suggested Citation

  • Regimantas Čiupaila & Mifodijus Sapagovas & Kristina Pupalaigė & Gailė Kamilė Šaltenienė, 2025. "On Error Estimation and Convergence of the Difference Scheme for a Nonlinear Elliptic Equation with an Integral Boundary Condition," Mathematics, MDPI, vol. 13(5), pages 1-20, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:873-:d:1606154
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