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- W39752421 abstract "This chapter discusses the solution of the differential equation by a finite linear combination of known functions. These known functions, usually called the basis functions, have the common property that they are relatively simple: polynomials, trigonometric functions, and, most importantly, spline functions. The solution is considered as lying in some appropriate (infinite-dimensional) function space, and one attempts to obtain an approximate solution that lies in the finite-dimensional subspace that is determined by the basis functions. The projection of the solution onto the finite-dimensional subspace is the approximate solution. For the purpose of approximating solutions to differential equations—and for many other situations—it is necessary that the approximating functions be at least twice continuously differentiable. This is not possible with piecewise quadratics unless the data are such that a single quadratic will suffice." @default.
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- W39752421 date "1992-01-01" @default.
- W39752421 modified "2023-09-26" @default.
- W39752421 title "Is There More Than Finite Differences?" @default.
- W39752421 doi "https://doi.org/10.1016/b978-0-08-051669-1.50010-1" @default.
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