Implicit two-point block method with third and fourth derivatives for solving general second order ODEs
In this paper we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs). The method incorporates the first and second derivatives of f(x; y; y 0), which are the third and fourth derivatives of the solution. The method is der...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Horizon Research Publishing
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/80180/1/Implicit%20Two-point%20block%20method%20with%20third%20and%20fourth%20Derivatives%20for%20Solving%20General%20Second%20Order%20ODEs.pdf http://psasir.upm.edu.my/id/eprint/80180/ https://www.google.com/search?client=firefox-b-d&q=Implicit+Two-point+block+method+with+third+and+fourth+Derivatives+for+Solving+General+Second+Order+ODEs |
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| Summary: | In this paper we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs). The method incorporates
the first and second derivatives of f(x; y; y 0), which are
the third and fourth derivatives of the solution. The method is
derived using Hermite Interpolating Polynomial as the basic
function. A performance comparison of the two-point block
method is compared in term of accuracy to several existing
methods, which have order almost equal or higher than that of the new method. Numerical results interpret the accuracy and efficacy of the new method. Application of the new method is discussed. |
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