Direct Computation of Operational Matrices for Polynomial Bases

الملخص EN

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.