加權基本不振盪法的概念是用每個網格的函數平均值來求解。由於無法找到使得兩個線性多項式的組合得到三階精確度的線性權，所以我們利用他們的反導函數來求得線性權函數。積分基礎加權基本不振盪法是用加權函數組合兩個線性多項式的反導函數來得到三階精確度。這方法利用到三個網格的函數平均值與加權函數。數值結果顯示出在平滑問題時能有三階精確度，而在不平滑問題時，也能有不錯的結果。

A Weighted Essentially Non-Oscillatory (WENO) reconstruction tech-
nique is developed that converts cell-averages on one grid to another grid
to high order. Since we can not combine two linear polynomials with linear
weights to obtain the third order accuracy, we take the whole computation to
its primitive level. We de ne an integral base CWENO3 scheme that com-
bines two primitive functions of the linear polynomials to obtain third order
accuracy. The new scheme uses a compact stencil of three cell-averages, and
weight functions are used. Numerical results show that this scheme is third
order accurate for smooth problems and gives good results for non-smooth
problems.

[Thesis Approval Sheet + i]
[摘要 +Š ii]
[Abstract + iii]
[1 Introduction + 1]
[2 The reconstruction technique + 3]
[2.1 The integral base WENO reconstruction process + 4]
[2.2 Modi cation of the weight functions for non-smoothness + 6]
[3 An integral base WENO method for one dimensional hyperbolic conservation law + 9]
[3.1 Flux evaluation in time using Runge-Kutta with natural continuous extension + 10]
[3.2 Summary of the scheme + 12]
[4 Numerical Results + 13]
[4.1 Example 1, constant linear transport + 13]
[4.2 Example 2, Shu' s linear test + 14]
[4.3 Example 3, Burgers' equation + 17]
[5 Conclusions + 19]
[References + 20]

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