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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| التنسيق: | أطروحة |
| اللغة: | English |
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2016
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| الوصول للمادة أونلاين: | http://psasir.upm.edu.my/id/eprint/66847/1/IPM%202016%2018%20IR.pdf |
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my-upm-ir.668472019-02-04T01:40:03Z Multistep block methods for solving volterra integro-differential equations of second kind 2016-06 Mohamed, Nurul Atikah 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. Volterra equations Integro-differential equations 2016-06 Thesis http://psasir.upm.edu.my/id/eprint/66847/ http://psasir.upm.edu.my/id/eprint/66847/1/IPM%202016%2018%20IR.pdf text en public masters Universiti Putra Malaysia Volterra equations Integro-differential equations |
| institution |
Universiti Putra Malaysia |
| collection |
PSAS Institutional Repository |
| language |
English |
| topic |
Volterra equations Integro-differential equations |
| spellingShingle |
Volterra equations Integro-differential equations Mohamed, Nurul Atikah Multistep block methods for solving volterra integro-differential equations of second kind |
| description |
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. |
| format |
Thesis |
| qualification_level |
Master's degree |
| author |
Mohamed, Nurul Atikah |
| author_facet |
Mohamed, Nurul Atikah |
| author_sort |
Mohamed, Nurul Atikah |
| title |
Multistep block methods for solving volterra integro-differential equations of second kind |
| title_short |
Multistep block methods for solving volterra integro-differential equations of second kind |
| title_full |
Multistep block methods for solving volterra integro-differential equations of second kind |
| title_fullStr |
Multistep block methods for solving volterra integro-differential equations of second kind |
| title_full_unstemmed |
Multistep block methods for solving volterra integro-differential equations of second kind |
| title_sort |
multistep block methods for solving volterra integro-differential equations of second kind |
| granting_institution |
Universiti Putra Malaysia |
| publishDate |
2016 |
| url |
http://psasir.upm.edu.my/id/eprint/66847/1/IPM%202016%2018%20IR.pdf |
| _version_ |
1747812415899172864 |