Numerical methods for a coupled system of differential equations arising from a thermal ignition problem

2012 ◽  
Vol 29 (1) ◽  
pp. 251-279 ◽  
Author(s):  
C.V. Pao ◽  
Yu-Hsien Chang ◽  
Guo-Chin Jau
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Coupled System ◽  
Thermal Ignition ◽  
System Of Differential Equations

scholarly journals New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II

2018 ◽  
Vol 1 (3) ◽  
pp. 30 ◽  
Author(s):  
Hussein ALKasasbeh ◽  
Irina Perfilieva ◽  
Muhammad Ahmad ◽  
Zainor Yahya
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Trapezoidal Rule ◽  
Approximation Methods ◽  
System Of Differential Equations ◽  
Fuzzy Transform ◽  
Fuzzy Partition ◽  
Fuzzy Approximation ◽  
One Step ◽  
Basic Functions

In this research, three approximation methods are used in the new generalized uniform fuzzy partition to solve the system of differential equations (SODEs) based on fuzzy transform (FzT). New representations of basic functions are proposed based on the new types of a uniform fuzzy partition and a subnormal generating function. The main properties of a new uniform fuzzy partition are examined. Further, the simpler form of the fuzzy transform is given alongside some of its fundamental results. New theorems and lemmas are proved. In accordance with the three conventional numerical methods: Trapezoidal rule (one step) and Adams Moulton method (two and three step modifications), new iterative methods (NIM) based on the fuzzy transform are proposed. These new fuzzy approximation methods yield more accurate results in comparison with the above-mentioned conventional methods.

scholarly journals Note On Cowling'S Method In The Theory Of Non-Radial Oscillations Of Massive Stars

1966 ◽  
Vol 19 (3) ◽  
pp. 467 ◽  
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Massive Stars ◽  
System Of Differential Equations ◽  
Complicated System

The study of non-radial adiabatic oscillations of stars requires the solution of a complicated system of differential equations and the extensive use of numerical methods.

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