# Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations

Our main contribution in the thesis is the development of a new block method which is called diagonally implicit two point block backward differentiation formulas of order two (DI2BBDF(2)), order three (DI2BBDF(3)) and order four (DI2BBDF(4)) for solving stiff ordinary differential equations (ODEs)...

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Main Author: Thesis English 2014 http://psasir.upm.edu.my/id/eprint/70475/1/FS%202014%2049%20IR.pdf No Tags, Be the first to tag this record!
id my-upm-ir.70475 uketd_dc my-upm-ir.704752019-10-30T03:26:27Z Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations 2014-01 Mohd Zawawi, Iskandar Shah Our main contribution in the thesis is the development of a new block method which is called diagonally implicit two point block backward differentiation formulas of order two (DI2BBDF(2)), order three (DI2BBDF(3)) and order four (DI2BBDF(4)) for solving stiff ordinary differential equations (ODEs) and fuzzy differential equations (FDEs). This method is constructed to compute multiple approximations concurrently in a block using various back values. The performance of the method is compared with existing methods. Furthermore, the convergence and stability properties of the method are investigated. The strategy of choosing suitable step size is also discussed. This thesis also explored the numerical solution of first order FDEs. The fully implicit two point block backward differentiation formulas of order three (FI2BBDF(3)) is reviewed and modified in fuzzy version for solving fuzzy initial value problems (FIVPs) under a new interpretation of Hukuhara Differentiability Theorem (HDT). Based on HDT, the exact and approximated solutions for two cases are compared to investigate the accuracy of the method. Finally, the derived method is modified in fuzzy version for solving FIVPs under HDT. The efficiency of the method is compared with several existing methods. In conclusion, the proposed method can be an alternative method for solving stiff ODEs and FDEs. Stiff computation (Differential equations) Differential equations - Numerical solutions 2014-01 Thesis http://psasir.upm.edu.my/id/eprint/70475/ http://psasir.upm.edu.my/id/eprint/70475/1/FS%202014%2049%20IR.pdf text en public masters Universiti Putra Malaysia Stiff computation (Differential equations) Differential equations - Numerical solutions Universiti Putra Malaysia PSAS Institutional Repository English Stiff computation (Differential equations) Differential equations - Numerical solutions Stiff computation (Differential equations) Differential equations - Numerical solutions Mohd Zawawi, Iskandar Shah Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations Our main contribution in the thesis is the development of a new block method which is called diagonally implicit two point block backward differentiation formulas of order two (DI2BBDF(2)), order three (DI2BBDF(3)) and order four (DI2BBDF(4)) for solving stiff ordinary differential equations (ODEs) and fuzzy differential equations (FDEs). This method is constructed to compute multiple approximations concurrently in a block using various back values. The performance of the method is compared with existing methods. Furthermore, the convergence and stability properties of the method are investigated. The strategy of choosing suitable step size is also discussed. This thesis also explored the numerical solution of first order FDEs. The fully implicit two point block backward differentiation formulas of order three (FI2BBDF(3)) is reviewed and modified in fuzzy version for solving fuzzy initial value problems (FIVPs) under a new interpretation of Hukuhara Differentiability Theorem (HDT). Based on HDT, the exact and approximated solutions for two cases are compared to investigate the accuracy of the method. Finally, the derived method is modified in fuzzy version for solving FIVPs under HDT. The efficiency of the method is compared with several existing methods. In conclusion, the proposed method can be an alternative method for solving stiff ODEs and FDEs. Thesis Master's degree Mohd Zawawi, Iskandar Shah Mohd Zawawi, Iskandar Shah Mohd Zawawi, Iskandar Shah Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations Universiti Putra Malaysia 2014 http://psasir.upm.edu.my/id/eprint/70475/1/FS%202014%2049%20IR.pdf 1747812846692990976