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Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be. This book is concerned with the investigation of the abo

Linear operators. --- Operator equations. --- Equations, Operator --- Differential equations, Partial --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory

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Functional analysis --- Banach [Espaces de ] --- Banach [Ruimten van ] --- Banach spaces --- Banach spaces. --- 51 --- Operator equations --- Equations, Operator --- Differential equations, Partial --- Functions of complex variables --- Generalized spaces --- Topology --- Mathematics --- 51 Mathematics

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Iterative methods (Mathematics) --- Operator equations --- Numerical solutions --- Nonlinear operators --- -517.983 --- 519.6 --- Equations, Operator --- Differential equations, Partial --- Operators, Nonlinear --- Operator theory --- Iteration (Mathematics) --- Numerical analysis --- Linear operators. Linear operator equations --- Computational mathematics. Numerical analysis. Computer programming --- Nonlinear operators. --- Numerical solutions. --- Iterative methods (Mathematics). --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.983 Linear operators. Linear operator equations --- 517.983 --- Newton-Raphson method --- Newton, Méthode de --- Analyse fonctionnelle non linéaire --- Nonlinear functional analysis --- Newton, Méthode de --- Analyse fonctionnelle non linéaire. --- Newton, Méthode de. --- Nonlinear functional analysis. --- Newton-Raphson method. --- Point fixe, Théorème du --- Operator equations - Numerical solutions --- Equations non lineaires --- Analyse en dimension infinie --- Approximation des solutions

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Operator theory --- Iterative methods (Mathematics) --- Operator equations --- 517.983 --- 519.6 --- 681.3 *G18 --- 681.3*G17 --- 681.3*G19 --- Equations, Operator --- Differential equations, Partial --- Iteration (Mathematics) --- Numerical analysis --- Linear operators. Linear operator equations --- 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) --- Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) --- 681.3*G19 Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) --- 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 --- 517.983 Linear operators. Linear operator equations --- Équations à opérateurs. --- Analyse numérique. --- Équations à opérateurs. --- Analyse numérique. --- Analyse fonctionnelle non linéaire --- Nonlinear functional analysis --- Analyse fonctionnelle non linéaire. --- Opérateurs, Théorie des --- Analyse fonctionnelle non linéaire. --- Opérateurs, Théorie des