Tasks in Computations

 

Shao-Yuan Huang and Shin-Hwa Wang

 

 

Introduction

These works contain computational algorithms and results which support the paper " On S-shaped bifurcation curves for a two-point boundary value problem arising in a theory of thermal explosion" by Shao-Yuan Huang, Shin-Hwa Wang. We divide this project into several tasks explaining the detail of these computations that appear in Appendix. In each task, we give a code and output (not all) to illustrate these complex computations. Readers can run these codes by Maple 16 to check the computations. These computations which are carried out by computer are based on symbolic and exact integer computations. However, in the sake of convenience, these outputs are displayed in numerical form.

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In Step1 of proof of Lemma 4.2

Task 1  For , we compute that

 

 ,

 ,

 

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In Step1 of proof of Lemma 4.2

Task 2  For , we compute that

 

 ,

 ,

 

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In Step2 of proof of Lemma 4.2

Task 3  For , we compute that

 

 and    (View the detail)

 

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In Part (i) of proof of Lemma 4.3

Task 4  For , we compute that

 

  (View the detail)

 

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In Part (i) of proof of Lemma 4.3

Task 5  For , we compute that

 

 

 

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In Part (ii) of proof of Lemma 4.3

Task 6  For , we compute that

 

 

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