Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions
Sadybekov M.A. Pankratova I.N.
October 2022MDPI
Mathematics
2022#10Issue 20
For a nonlocal initial-boundary value problem for a one-dimensional heat equation with not strongly regular boundary conditions of general type, an approximate difference scheme with weights is constructed. A correct and stable algorithm for the numerical solving of the difference problem is proposed. It is proven that the difference scheme with weights is stable and its solution converges to the exact solution of the differential problem in the grid (Formula presented.) -norm. Stability conditions are established. An estimate of the numerical solution with respect to the initial data and the right-hand side of the difference problem is given.
boundary value problems , difference equations , heat conduction equation , non-local problems , not strongly regular boundary conditions , numerical algorithms , partial differential equations , stability and convergence
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Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Depatment of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Depatment of Mechanics and Mathematics
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