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from Part II - Numerical Methods
Published online by Cambridge University Press: 18 February 2021
A central goal of scientists and engineers is obtaining solutions of the differential equations that govern their physical systems.This can be done numerically for large and/or complex systems using finite-difference methods, finite-element methods, or spectral methods.This chapter gives an introduction and the formal basis for these methods, with particular emphasis on finite-difference methods.Second-order partial differential equations are classified as elliptic, parabolic, or hyperbolic, and the numerical methods developed for such equations must be faithful to their mathematical properties.
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