Scientific Computing and Differential Equations: An Introduction to Numerical Methods
Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context.
This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level.
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additional algorithm applied approach approximate approximate solution assume basis becomes bound boundary conditions called carry Chapter coefficient matrix column complex consider constant continuous convergence corresponding defined definite derivatives determined diagonal difference differential equations discretization error discussed eigenvalues eigenvectors elements evaluated exact solution example Exercise factorization Figure finite formula function Gaussian elimination give given grid points Hence holds important initial conditions integration interchange interpolating interval iteration known least linear system mathematical method multiplications non-zero nonlinear Note obtain operations orthogonal orthogonal matrix partial particular points polynomial positive possible problem reduced requires roots rule satisfies Show shown side solution solve space stability step Suppose symmetric symmetric matrix system of equations Theorem tridiagonal unknowns usually variables vector verify write zero