“collocation methods”的概念、定义、翻译、参考文献-科学参考

collocation methods

Computer

单词	collocation methods
释义	collocation methods Computer An important approach to the numerical solution of ordinary differential and integral equations. Approximations are obtained on the basis that the equation is satisfied exactly at a particular set of points in the given problem range. For example, for $y ″ = f (x, y, y'), a \leq x \leq b,$ an approximation $P (x) = \sum_{i = 1}^{n} α_{i} ϕ_{i} (x)$ can be obtained from a suitable set of orthogonal functions ϕ‎_i(x) by choosing the coefficients α‎_i for which $P^{″} (x_{i}) = f (x_{i}, P (x_{i}), P^{'} (x_{i})),$ for some set of collocation points $a \leq x_{1} < x_{2} < \dots < x_{n} \leq b$ Initial conditions and boundary conditions may also be incorporated into the process.
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