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**Direct computation of operational matrices for polynomial bases.**
*(English)*
Zbl 1198.65121

Summary: Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

### MSC:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

34B05 | Linear boundary value problems for ordinary differential equations |

### Keywords:

boundary value problems; operational matrices; polynomial bases; integration; differentiation; linear operation
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\textit{O. Guimarães} et al., Math. Probl. Eng. 2010, Article ID 139198, 12 p. (2010; Zbl 1198.65121)

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