Solving higher order delay differential equations with boundary conditions using multistep block method
In this thesis, we derived two numerical methods called two point diagonally multistep block method order four and order five with the approach of predictorcorrector technique to solve higher order delay differential equations (DDEs) with boundary conditions. Shooting technique by using the Newto...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
2021
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/98787/1/IPM%202021%2015%20%20-%20IR.pdf |
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| Summary: | In this thesis, we derived two numerical methods called two point diagonally
multistep block method order four and order five with the approach of predictorcorrector
technique to solve higher order delay differential equations (DDEs) with
boundary conditions. Shooting technique by using the Newton’s like method is
implemented to solve the boundary value problems (BVPs). This thesis begins with
solving second order DDEs with constant, pantograph and time dependent delay
type by using both methods. Then, those methods are extended to solve third order
DDEs with constant and pantograph delay type.
The approach used to solve constant delay type is by taking the previously calculated
solutions at the delay terms while for pantograph and time dependent delay
types, the approaches are by using the Lagrange interpolation to approximate the
solutions at the delay terms. The derivatives present in the problems at the delay
terms will be approximated by using the finite difference method. The analysis
of both methods in terms of order, local truncation error and stability are also
investigated. Two stability test equations are used to analyze the stability regions of
the block methods.
Several numerical problems are illustrated to solve by using C programming. The
accuracy of the methods in terms of maximum and average errors along with
the total function calls, total iteration steps, total guessing numbers for shooting
technique are discussed and compared with the previous methods. In conclusion, the higher order DDEs with boundary conditions can be solved by
using the proposed block methods based on the analysis of the methods and their
numerical results. |
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