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How to use Jacobian in BEAM-WARMING METHOD

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Old   July 20, 1999, 05:50
Default How to use Jacobian in BEAM-WARMING METHOD
Yogesh Talekar
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Can anybody help me with this. I am solving 1-D equations of the form dU/dt + dF/dx = 0 using Beam-Warming method. After finding jacoboan which is 3X3 i get them in the form dU/dt + B * dU/dx = 0 form I have denoted the elements of matrix as

B11, B12, B13,

B21, B22, B23

B31, B32, B33

After using Finite difference the equation becomes tri-diagonal and can be solved using THOMSAS algorithm

But there are calculations like B1[i] * U1[i] So should i calculate such term like

(B11[i]*B12[i]* B13[i]) * U1[i]

Or some thing else is needed to be done here? Can Anybody help?
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