Sentence examples for matrices of derivative from inspiring English sources

Therefore, the operational matrices of derivative D and Fibonacci coefficient matrix F are introduced in the main body of the study.

Some other studies in [21, 22] employ tau operational matrices of derivatives for solving the same type of equations.

The operational matrices of derivatives and integrals are frequently used in the literature to solve fractional-order differential equations.

For example, the authors in [6], employed the tau operational matrices of derivatives of Chebyshev polynomials of the second kind for handling the singular Lane-Emden type equations.

The operational matrices of derivatives of exponential Legendre and exponential Chebyshev functions of the first and second kinds, which often appear in conjunction with such spectral methods in the literature, may be obtained as special cases of the operational matrix of exponential Jacobi functions by taking the corresponding spacial cases of the exponential Jacobi functions parameters θ and ϑ.

In this paper, we derived the operational matrix of derivative of exponential Jacobi functions.

Here we shall give the derivation of a new operational matrix of derivative of the exponential Jacobi functions, which is essential to our numerical method.

Our approach based on Chebyshev Tau technique utilizes Chebyshev polynomials and the associated operational matrix of derivative.

The operational matrix of derivative of Chebyshev wavelets is introduced.

This paper presented the operational matrix of derivative of discrete Hahn polynomials.

By use of orthonormal Bernoulli polynomials as basis and the operational matrix of derivative of these functions, we convert such problems to an algebraic system.