Solving second order boundary value problem by shooting technique using backward difference formulae
In this thesis, the direct implicit multistep method presented in the form of backward difference formula are developed for solving directly two point boundary value problems (BVPs). This method will solve the nonlinear second order BVPs by shooting technique using constant and variable step size. N...
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| Format: | Thesis |
| Language: | English |
| Published: |
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/26514/1/IPM%202011%2020R.pdf http://psasir.upm.edu.my/id/eprint/26514/ |
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| Summary: | In this thesis, the direct implicit multistep method presented in the form of backward difference formula are developed for solving directly two point boundary value problems (BVPs). This method will solve the nonlinear second order BVPs by shooting technique using constant and variable step size. Newton’s method is considered as a procedure for solving the nonlinear equations and the convergence of the shooting technique. Most of the existing researches involved BVPs will reduce the problem to a system of first order ordinary differential equations (ODEs). This approach is very well established but it obviously will enlarge the system of first order equations. However, the direct multistep method in this thesis will be utilized to obtain series solutions of the initial value problems directly without reducing to first order equations. The coefficients of the developed method will be stored in the code in the form of backward difference formula. The codes were executed in UNIX operating system and the algorithms were written in C language. The numerical results showed that the performance of the developed method is acceptable in terms of maximum error and number of iterations when solving second order nonlinear boundary value problem |
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