03707nmm a2200337 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001400139245012200153250001700275260004000292300003200332505100200364653002601366653002301392653002301415653002701438653001301465700002901478700002601507710003401533041001901567989003801586490004601624856007201670082000801742520161901750EB000616916EBX0100000000000000046999800000000000000.0cr|||||||||||||||||||||140122 ||| eng a97814471037761 aEvans, G.00aNumerical Methods for Partial Differential EquationshElektronische Ressourcecby G. Evans, J. Blackledge, P. Yardley a1st ed. 2000 aLondonbSpringer Londonc2000, 2000 aXII, 290 pbonline resource0 a1. Background Mathematics -- 1.1 Introduction -- 1.2 Vector and Matrix Norms -- 1.3 Gerschgorin’s Theorems -- 1.4 Iterative Solution of Linear Algebraic Equations -- 1.5 Further Results on Eigenvalues and Eigenvectors -- 1.6 Classification of Second Order Partial Differential Equations -- 2. Finite Differences and Parabolic Equations -- 2.1 Finite Difference Approximations to Derivatives -- 2.2 Parabolic Equations -- 2.3 Local Truncation Error -- 2.4 Consistency -- 2.5 Convergence -- 2.6 Stability -- 2.7 The Crank-Nicolson Implicit Method -- 2.8 Parabolic Equations in Cylindrical and Spherical Polar Coordinates -- 3. Hyperbolic Equations and Characteristics -- 3.1 First Order Quasi-linear Equations -- 3.2 Lax-Wendroff and Wendroff Methods -- 3.3 Second Order Quasi-linear Hyperbolic Equations -- 3.4 Reetangular Nets and Finite Difference Methods for Second Order Hyperbolic Equations -- 4. Elliptic Equations -- 4.1 Laplace’s Equation -- 4.2 Curved Boundaries -- 4.3 Solution of Spa aMathematical analysis aNumerical analysis aNumerical Analysis aAnalysis (Mathematics) aAnalysis1 aBlackledge, J.e[author]1 aYardley, P.e[author]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aSpringer Undergraduate Mathematics Series uhttps://doi.org/10.1007/978-1-4471-0377-6?nosfx=yxVerlag3Volltext0 a518 aThe subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. James Clerk Maxwell, for example, put electricity and magnetism into a unified theory by establishing Maxwell's equations for electromagnetic theory, which gave solutions for prob lems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechanical processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forecasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics