PUBLISHED PAPERS #04.09
| Gulshan Shafiyeva, Vagif Ibrahimov. On Some Ways to Construct Multistep Methods with High Degree and Their Application to Solving Initial-Value Problem for Odes of the Second Order |
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| Abstract. Among the numerical methods constructed for solving initial-value problems for Ordinary Differential Equations (ODEs), the most popular are the Runge-Kutta and Adams methods. Each of these methods has its advantages and disadvantages. For comparison of Runge-Kutta and Adams methods with the multistep methods have used the conception of stability, degree, region of stability, and volume of computational works. As is known many scientists have investigated the numerical solution of the initial-value problem of ODEs of the first and second order, since the Age of Newton. Some specialists tried to apply some modification of methods, which are constructed for solving initial-value problems for the ODEs of the first and second order. Considering the actuality of the above-suggested numerical methods, here have compared the known classes’ methods and constructed the new methods on the intersection of the above-mentioned methods. To use above mentioned, here have constructed Multistep second and third derivatives Methods and proven the advantages of the suggested methods. |
| Keywords: Initial-value problem, Stability and Degree, Multistep second and third derivative methods |
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| DOI: https://doi.org/10.30546/MaCoSEP2025.1052 |