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Numerical Iteration Method A numerical iteration method or simply iteration method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. Boundary value problems and the finite element method 240 48. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. Part Two covers the fundamentals of algorithms and numerical analysis at a level that allows students to quickly apply results in practical settings. A numerical method is one of the algorithms which involved with computer programming. The book uses Mathematica to illustrate the algorithms, but in real life people would either use built-in functions in Mathematica or use a separate software package, and would not write their own algorithms. 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