| 1 |
This give Iterative equation if we use k to label time steps
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| 2 |
c1 yk+1(x,y) = ( y"k"(x+h,y) + y"k"(x-h,y)+y"k"(x,y+h)+y"k"(x,y-h))/4
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| 3 |
- c2 y"k"(x,y)
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| 4 |
where c1 + c2 = 1
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| 5 |
and the value of c1,c2 depend on K,h and dt.
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| 6 |
as dt is arbitary, we can choose c1
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| 7 |
(and hence c2 = 1 - c1 ) to optimize convergence.
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| 8 |
We use cryptic notaation "k" to repreprent various possible choices for evaluating time on right hand side. Simplest is "k" = k but choices are k, k+1 or linear combinations which can vary for different x values.
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