Uniform Schemes

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

Chapter Chapter 1 in The Method of Fractional Steps, 1971, pp 1-16 from Springer

Abstract: Abstract In this course of lectures we consider primarily the system of differential equations of the type 1.1.1 $$ \frac{{\partial {\mkern 1mu} u\left( {x,t} \right)}}{{\partial t}} = {\mkern 1mu} L\left( D \right){\mkern 1mu} u\left( {x,t} \right) + {\mkern 1mu} f\left( {x,t} \right),$$ where $$ u\left( {x,t} \right) = {\mkern 1mu} \left\{ {{u_1}\left( {{x_1}, \ldots ,{x_m},t} \right),{u_2}{\mkern 1mu} \left( {{x_1}, \ldots ,{x_m},t} \right), \ldots ,{u_n}{\mkern 1mu} \left( {{x_1}, \ldots ,{x_m},t} \right)} \right\}, $$ $$ f\left( {x,t} \right) = \left\{ {{f_1}\left( {{x_1}, \ldots ,{x_m},t} \right),{f_2}{\mkern 1mu} \left( {{x_1}, \ldots ,{x_m},t} \right), \ldots ,{f_n}{\mkern 1mu} \left( {{x_1}, \ldots ,{x_m},t} \right)} \right\} $$ are vector functions of the vector space variable x = (x1,…, xm) and of time t; L(D) is a matrix linear differential operator with variable coefficients, D = {D i }, D i = ∂/∂x i , i = 1,…, m.

Keywords: Cauchy Problem; Difference Scheme; Dispersion Equation; Matrix Factorization; Heat Conduction Equation (search for similar items in EconPapers)
Date: 1971
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DOI: 10.1007/978-3-642-65108-3_1

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