This article examines numerical methods for solving boundary value problems for parabolic differential equations, which are widely used in modeling physical processes such as the filtration of oil, gas, and water in porous media, as well as heat transfer processes.The primary focus is on the differentialdifference method, which is characterized by its high accuracy and ease of programming.The theoretical aspects of the method are presented, including algorithmic implementation, the use of the differential sweep method, and an analysis of the stability of the computational process.Special attention is given to the advantages of the differential-difference approach, such as the ability to automatically fulfill internal conditions during phase transitions, ensure absolute computational stability, and simplify programming.The article also describes the solution algorithm, which includes a longitudinal-transverse scheme that enables efficient problem-solving using parallel computations.Additionally, numerical calculation results are provided, including comparisons with analytical solutions that demonstrate the method's high accuracy.It is shown that the developed algorithms can be easily adapted for solving other classes of problems, making them a universal tool for numerical modeling in computational mathematics.The conclusions are supported by graphical results and error analysis, confirming the reliability of the proposed approach.
| Jurnal | ТАТУ хабарлари |
|---|---|
| Nashr sanasi | 2024-12-29 |
| DOI | 10.61663/244tuitmct3 |
DOI: 10.61663/244tuitmct3 · Maqolaning asl sahifasi
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