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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