Multistep block method for solving second and third order boundary value problems with Robin and mixed type boundary conditions
This thesis investigates on the numerical solutions for solving two-point and multipoint boundary value problems (BVPs) subject to Robin and mixed boundary conditions. The BVPs are solved directly using the new developed two-point diagonally implicit multistep block method in the form of Adams ty...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
2020
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/104714/1/NADIRAH%20BINTI%20MOHD%20NASIR%20-%20IR.pdf |
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| Summary: | This thesis investigates on the numerical solutions for solving two-point and
multipoint boundary value problems (BVPs) subject to Robin and mixed boundary
conditions. The BVPs are solved directly using the new developed two-point
diagonally implicit multistep block method in the form of Adams type formula.
Constant and variable step size strategy are employed for solving two-point
second-order BVPs. Meanwhile, the computed solutions for two-point and
multipoint third-order BVPs are limit to constant step size. Shooting technique is
implemented in order to solve the BVPs. The initial estimate values are obtained
using the Newton’s divided difference interpolation method and Steffensen’s
method. Alternatively, the first derivative function is absence during the calculation
of guessing values compared to the shooting technique via the Newton’s method.
The analysis included order, error constants, consistency, zero-stability and
convergence are presented in describing the characteristics of the proposed methods.
All the computational procedures were undertaken using the C language in a
Code::Blocks 16.01 cross platform.
Numerical results showed significant findings where the proposed methods could
offer better accuracy results, less costly in terms of total function calls and faster in
timing compared to the existing methods.
In conclusion, the proposed methods and developed algorithms were shown to be
a reliable BVPs solver for solving two-point and multipoint BVPs subject to Robin
and mixed boundary conditions directly. |
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