Simple Schemes in Fractional Steps for the Integration of Parabolic Equations

N. N. Yanenko
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N. N. Yanenko: U.S.S.R. Academy of Sciences, Siberian Branch Computing Center

Chapter Chapter 2 in The Method of Fractional Steps, 1971, pp 17-41 from Springer

Abstract: Abstract The conditionally stable scheme (1.5.14) is unsymmetric. The approximation of the second derivative with respect to x is implicit, and with respect to y is explicit. Let us consider a symmetric modification of this scheme in which x and y interchange roles at each step: 2.1.1 $$\frac{{{u^{n + 1}} - {u^n}}}{\tau } = {\Lambda _1}\,{u^{n + 1}} + {\Lambda _2}\,{u^n}$$ $$\frac{{{u^{n + 2}} - {u^{n + 1}}}}{\tau } = {\Lambda _1}\,{u^{n + 1}} + {\Lambda _2}\,{u^{n + 2}}$$

Keywords: Parabolic Equation; Heat Conduction Equation; Fractional Step; Splitting Scheme; Mixed Derivative (search for similar items in EconPapers)
Date: 1971
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-65108-3_2

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DOI: 10.1007/978-3-642-65108-3_2

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