Differential Equations Lecture Work Solutions 298

Differential Equations Lecture Work Solutions 298 - 8.3...

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Unformatted text preview: 8.3 Irregular Mesh Problems 1. Develop a finite difference approximation with T.E. of O (∆y )2 for ∂T /∂y at point (i, j ) using Ti,j , Ti,j +1 , Ti,j +2 when the grid spacing is not uniform. 2. Determine the T.E. of the following finite difference approximation for ∂u/∂x at point (i, j ) when the grid space is not uniform: ui+1,j − (∆x+ /∆x− )2 ui−1,j − [1 − (∆x+ /∆x− )2 ] ui,j ∂u |i,j ≈ ∂x ∆x− (∆x+ /∆x− )2 + ∆x+ 298 ...
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