Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions
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 propose...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/20/3780 |
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| author | Makhmud A. Sadybekov Irina N. Pankratova |
| author_facet | Makhmud A. Sadybekov Irina N. Pankratova |
| author_sort | Makhmud A. Sadybekov |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>L</mi><mn>2</mn><mi>h</mi></msubsup></semantics></math></inline-formula>-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. |
| first_indexed | 2024-03-09T19:52:43Z |
| format | Article |
| id | doaj.art-f894fec6617a4ffbae97278680fe71c8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T19:52:43Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f894fec6617a4ffbae97278680fe71c82023-11-24T01:06:54ZengMDPI AGMathematics2227-73902022-10-011020378010.3390/math10203780Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary ConditionsMakhmud A. Sadybekov0Irina N. Pankratova1Institute of Mathematics and Mathematical Modeling, Almaty 050010, KazakhstanInstitute of Mathematics and Mathematical Modeling, Almaty 050010, KazakhstanFor 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>L</mi><mn>2</mn><mi>h</mi></msubsup></semantics></math></inline-formula>-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.https://www.mdpi.com/2227-7390/10/20/3780difference equationspartial differential equationsheat conduction equationnon-local problemsboundary value problemsnot strongly regular boundary conditions |
| spellingShingle | Makhmud A. Sadybekov Irina N. Pankratova Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions Mathematics difference equations partial differential equations heat conduction equation non-local problems boundary value problems not strongly regular boundary conditions |
| title | Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions |
| title_full | Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions |
| title_fullStr | Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions |
| title_full_unstemmed | Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions |
| title_short | Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions |
| title_sort | correct and stable algorithm for numerical solving nonlocal heat conduction problems with not strongly regular boundary conditions |
| topic | difference equations partial differential equations heat conduction equation non-local problems boundary value problems not strongly regular boundary conditions |
| url | https://www.mdpi.com/2227-7390/10/20/3780 |
| work_keys_str_mv | AT makhmudasadybekov correctandstablealgorithmfornumericalsolvingnonlocalheatconductionproblemswithnotstronglyregularboundaryconditions AT irinanpankratova correctandstablealgorithmfornumericalsolvingnonlocalheatconductionproblemswithnotstronglyregularboundaryconditions |