Block backward differentiation formula with off-step points for solving first order stiff ordinary differential equations
This thesis compiles four new numerical methods that are successfully derived and presented based on Block Backward Differentiation Formulas (BBDFs) for the numerical solution of stiff Ordinary Differential Equations (ODEs). The first method is a one-point block order three BDF with one off-step...
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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/98058/1/FS%202020%2039%20UPMIR.pdf |
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| Summary: | This thesis compiles four new numerical methods that are successfully derived and
presented based on Block Backward Differentiation Formulas (BBDFs) for the numerical
solution of stiff Ordinary Differential Equations (ODEs). The first method
is a one-point block order three BDF with one off-step point. The second method is
developed by increasing the order of one-point block BDF with one off-step point to
order four in order to increase the accuracy of the approximate solution. The third
and fourth method are extension of the one-point block to two-point block BDFs
method with off-step points.
The order and error constant of the methods are determined. Conditions for convergence
and stability properties for all newly developed methods are discussed and
verified so that the derived methods are suitable for solving stiff ODEs. Comparisons
of stability regions are also investigated with the existing methods. Newton’s
iteration method is implemented in all developed methods. Numerical results are
presented to verify the accuracy of the block BDF with off-step points for solving
stiff ODEs and compared to the existing related methods of similar properties.
The final part of the thesis is by applying the formulated methods in solving the
global warming problem and home heating problem as the example that the derived
method can be applied to solve a real life application. In conclusion, by adding offstep
point, the accuracy is improved. Therefore, it can be an alternative solver for
solving first order stiff ODEs. |
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