Diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations
This paper aims to select the best value of the parameter ρ from a general set of linear multistep formulae which have the potential for efficient implementation. The ρ -Diagonally Implicit Block Backward Differentiation Formula ( ρ -DIBBDF) was proposed to approximate the solution for stiff Ordinar...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Multidisciplinary Digital Publishing Institute
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/82778/ http://psasir.upm.edu.my/id/eprint/82778/1/Diagonally_Implicit_Block_Backward_Differentiation.pdf |
| Summary: | This paper aims to select the best value of the parameter ρ from a general set of linear multistep formulae which have the potential for efficient implementation. The ρ -Diagonally Implicit Block Backward Differentiation Formula ( ρ -DIBBDF) was proposed to approximate the solution for stiff Ordinary Differential Equations (ODEs) to achieve the research objective. The selection of ρ for optimal stability properties in terms of zero stability, absolute stability, error constant and convergence are discussed. In the diagonally implicit formula that uses a lower triangular matrix with identical diagonal entries, allowing a maximum of one lower-upper (LU) decomposition per integration stage to be performed will result in substantial computing benefits to the user. The numerical results and plots of accuracy indicate that the ρ -DIBBDF method performs better than the existing fully and diagonally Block Backward Differentiation Formula (BBDF) methods. |
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