Abstract
Matrix differential equations are at the heart of many science and engineering problems. In this paper, a procedure based on higher-order matrix splines is proposed to provide the approximated numerical solution of special nonlinear third-order matrix differential equations, having the form Y(3)(x)=f(x,Y(x)). Some numerical test problems are also included, whose solutions are computed by our method.
Highlights
In different areas of engineering and applied science, such as those described in [1,2], third-order ordinary differential equation arise in the form of: Real-Herráiz, T
For the resolution of this type of equation, various different numerical techniques have been developed and exist in the literature [3,4,5,6,7]. They frequently depend on very well-known numerical methods, once the original equations have been converted into a system of first-order ordinary differential equations
We present a new algorithm for solving matrix third-order differential equations of the type shown in Equation (1)
Summary
In different areas of engineering and applied science, such as those described in [1,2], third-order ordinary differential equation arise in the form of: Real-Herráiz, T. For the resolution of this type of equation, various different numerical techniques have been developed and exist in the literature [3,4,5,6,7] They frequently depend on very well-known numerical methods, once the original equations have been converted into a system of first-order ordinary differential equations. We present a new algorithm for solving matrix third-order differential equations of the type shown in Equation (1). The derivative of a matrix A ∈ Cm×n with respect to a matrix B ∈ C p×q was defined by [13] as:. The derivative of the product of two matrices A ∈ Cm×n and B ∈ Cn×s with respect to another matrix C ∈ C p×q is given by:.
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