Multistep block methods for solving volterra integro-differential equations of second kind
Numerical solutions of Volterra integro-differential equations (VIDEs) by using multistep block methods are proposed in this thesis. The two point one-step block method, two point two-step block method and two point three-step block method are derived by using the Lagrange interpolating polyno...
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| 主要作者: | |
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| 格式: | Thesis |
| 语言: | English |
| 出版: |
2016
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| 主题: | |
| 在线阅读: | http://psasir.upm.edu.my/id/eprint/66847/1/IPM%202016%2018%20IR.pdf |
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| 总结: | Numerical solutions of Volterra integro-differential equations (VIDEs) by using multistep
block methods are proposed in this thesis. The two point one-step block
method, two point two-step block method and two point three-step block method
are derived by using the Lagrange interpolating polynomial. The generated multistep
block methods will estimate the solution of VIDEs at two points simultaneously
in a block by using constant step sizes. The source code for solving VIDEs are
developed by using C programming.
In VIDEs the unknown functions appear under the differential and integral sign, so
the combinations of multistep block methods with numerical quadrature rules are
applied. The multistep block methods are used to solve the ordinary differential
equation (ODE) part and quadrature rules are applied to calculate the integral part
of VIDEs. The method developed has solved for linear and nonlinear second kind
VIDEs.
The type of numerical quadrature rules used for solving the integral part of VIDEs
is of Newton-Cotes type. Thus, the quadrature rules of suitable order are used to be
paired with the multistep block methods. Two different approaches are proposed to
solve for two cases where kernel equal or not equal one. The stability region of the
combination methods are studied.
Numerical problems are presented to show the performance of the proposed method.
The results indicated that the proposed method is suitable for solving both linear and
nonlinear VIDEs. |
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