Sentence examples for using the operational matrix from inspiring English sources
One approach is based on converting differential equations into integral equations through integration, approximating various signals involved in the equation by truncated orthogonal series, and using the operational matrix of integration, to eliminate the integral operations [17].
3, and we will solve two fractional-order equations using the operational matrix in Sect.
By using the operational matrix of integration, we propose a new numerical method for linear fractional partial differential equation solving.
There are some papers in the literature about using the operational matrix of derivatives to solve differential equations [6, 18, 19].
In [21] Tripathi et al. presented an approximate solution of multi-term FDEs using the operational matrix of fractional integration of the generalized hat basis functions.
By using the operational matrix, the nonlinear fractional integro-differential equations are reduced to a system of algebraic equations which is solved through known numerical algorithms.
Using the operational matrices of block pulse functions, stochastic differential equations can be reduced to a system of algebraic equations.
By using the operational matrices for basis functions, spectral methods reduce the solution of fractional differential and integral equations into a solution of systems of algebraic equations which produce highly accurate solutions for these equations [22, 23, 30, 32].
Another technique applied to solve FDE is to use the operational matrix of fractional order [2, 6, 11, 17].
In this direction, Atabakzadeh et al. [19] used the operational matrix of Caputo fractional-order derivatives for Chebyshev polynomials, which was derived in [20] to solve a system of FDEs.
Since one of our aims in this paper is to solve FDEs under different types of local and non-local boundary conditions, we have to face some complicated situations, so to handle these situations we will use the operational matrix developed in the next theorem.
