Convergence Analysis of Block Implicit One Step Methods for Solving Differential

Cover Convergence Analysis of Block Implicit One Step Methods for Solving Differential
Convergence Analysis of Block Implicit One Step Methods for Solving Differential
Iris Marie Mack
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:= Xq +kh, iZ5} such that % = nr .
and £ m : n. Because of the mgnner in vvhich h is defined, v/e see that K tin For notational convenience let us define the following r-nd-dimensiunsl arrays: Uind, rf, ]:= [iiJ, k+ 1 "''. •••. Ild >:+r''' V, Uind, 0V=lzj/. -. Id/]^- 2(nc. M] " iSid>;+1^. ■•■, id>+r^r. Zjndo] ■= '=^, 0''". -. Ixi. O'^]'''' ror 1 . - , m i H and k = mil . - Also, let u: utilize the KronecKer" product notation to define the foUovving n-iatrice:. , which will be utilized to extrec
...t the equations correiDonding to the differentia] variaDles fron"! the difference equation? denned in M, 9): and P[r, d] = !^'r X lr, d.
Where l'\, B, and [v are defined as in equation (1. 8).
For each such grid of the form (3. 3), we can define the following difference schenrie: [nC[pH;]"' iU-nd.^l'^NiyU-l -t''C[nd;2(nd, m]"'P[nd;Zind, m-1 V^ - iV-nd, I •■ il ■•Is' ija^'-kri.. Io, »:+)■ ;i

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