Numerical Solution of Nonlinear Boundary Value Problems with Applications
A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems.
The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.
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accuracy analogous auxiliary equations boundary layer boundary value problems branching points calculated Chem Consider denoted dependence described Diﬂerential equations results Euler method evaluated Example false transient equations false transient method ﬁnd ﬁnite ﬁnite-difference approximation ﬁnite-difference method ﬁrst derivative ﬁrst-order differential equations ﬂow ﬂuid Green’s function heat and mass initial conditions initial guess initial proﬁle initial value problem Jacobian matrix linear algebraic linear algebraic equations linear boundary value mass transfer mesh points method of adjoints missing initial conditions modiﬁed multiple solutions NBVP Newton method Newton—Kantorovich method nonlinear boundary value numerical solution one-loop ordinary differential equations parameter partial differential equations rate of convergence reported in Table right-hand sides satisﬁed second-order differential equation Section set of differential set of linear shooting method solution of nonlinear solved structural matrix technique third-order tion tridiagonal tridiagonal matrix tubular reactor two-point boundary value variables yields