A new class of A-stable numerical techniques for ordinary differential equations: Application to boundary-layer flow
| Autor: | Muhammad Arif Shoaib, Yasir Nawaz |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Polynomial
maximum absolute error Renewable Energy Sustainability and the Environment Computer science Ode derivative(s) Grid interpolation darch-forchheimer flow Flow (mathematics) Approximation error Ordinary differential equation TJ1-1570 Applied mathematics a-stable Mechanical engineering and machinery Boundary value problem Interpolation |
| Zdroj: | Thermal Science, Vol 25, Iss 3 Part A, Pp 1665-1675 (2021) |
| ISSN: | 2334-7163 0354-9836 |
| DOI: | 10.2298/tsci190926097n |
| Popis: | The present attempt is made to propose a new class of numerical techniques for finding numerical solutions of ODE. The proposed numerical techniques are based on interpolation of a polynomial. Currently constructed numerical techniques use the additional information(s) of derivative(s) on particular grid point(s). The advantage of the presently proposed numerical techniques is that these techniques are implemented in one step and can provide highly accurate solution and can be constructed on fewer amounts of grid points but has the disadvantage of finding derivative(s). It is to be noted that the high order techniques can be constructed using just two grid points. Presently proposed fourth order technique is A-stable but not L-stable. The order and maximum absolute error are found for a fourth order technique. The fourth order technique is employed to solve the Darcy-Forchheimer fluid-flow problem which is transformed further to a third-order non-linear boundary value problem on the semi-infinite domain. |
| Databáze: | OpenAIRE |
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