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One of the leading experts in the field discusses recent developments in the numerical analysis of nonlinear equations involving a finite number of parameters. Shows how these equations can be developed on a differential geometric basis. Topics include equilibrium manifolds, path-tracing on manifolds, aspects of computational stability analysis, discretization errors of parameterized equations, and computational error assessment and related questions.

Differential equations, Nonlinear --- Equations --- Differentiable manifolds --- Numerical solutions --- numerical solutions --- -Differentiable manifolds --- -519.6 --- 681.3 *G18 --- 681.3*G17 --- 681.3*G4 --- Algebra --- Mathematics --- Differential manifolds --- Manifolds (Mathematics) --- Nonlinear differential equations --- Nonlinear theories --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- Differentiable manifolds. --- Numerical solutions. --- 681.3*G4 Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.6 --- Numerical analysis --- Graphic methods --- Differential equations, Nonlinear - Numerical solutions --- Equations - numerical solutions

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Numerical solutions of algebraic equations

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Numerical calculations

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Ordinary differential equations --- Differential equations --- Data processing. --- Differential equations - Data processing.