On the Approximated Solution of a Special Type of Nonlinear Third-Order Matrix Ordinary Differential Problem

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.

On solutions of second-order matrix polynomial equation of high degree

In this paper, we focus on discussing diagonal solutions and general solutions of second-order matrix polynomial equation of high degree in complex field. By characterizing some algebraic properties of the mentioned two types of the solutions, we present sufficient conditions that a general second-order matrix polynomial equation has diagonal solutions or general solutions. Analytic expressions of the solutions, as well as the corresponding algorithms for finding the solutions are provided. An example is given so as to verify the theoretical results we have derived.

Spectrum Matriks Detour dari Graf Roda dengan n +1 Titik W_n

Penelitian ini bertujuan untuk menentukan spectrum matriks detour dari graf roda dengan n+1 titik Wn. Spectrum dalam teori graf merupakan suatu topik menarik untuk dikaji dengan mempertemukan teori graf dan aljabar linear. Bentuk spectrum matriks detour adalah salah satu spectrum yang dapat ditentukan dalam graf roda. Matriks berordo (2 × n) yang terdiri dari nilai eigen berbeda dan banyak basis ruang eigen dari matriks terhubung langsung graf roda merupakan spectrum dari graf roda. Hasil penelitian ini menunjukkan bahwa langkah-langkah dalam menentukan spectrum matriks detour dari graf roda n+1 titik Wn, yaitu: menentukan graf roda dengan n + 1 titik Wn; menentukan detour, nilai eigen dan vektor eigen dari graf roda dengan n + 1 titik Wn,; melihat spectrum dan pola spectrum matriks detour dari graf roda n+1 titik Wn; pola yang didapat berupa dugaan kemudian dibuktikan dengan merumuskan suatu teorema yang dilengkapi dengan bukti. Kata Kunci: Spectrum, Matriks Detour, Graf RodaThis study aims to determine the spectrum of detour matrix from the wheel graph with n+1 point Wn. Spectrum in graph theory is an interesting topic to review by bringing together graph theory and linear algebra. The form of the spectrum of detour matrix is one of the spectrums that can be determined in the wheel graph. The order matrix (2 × n) which consists of different eigenvalues and many the eigen space base from matrix adjacent wheel graph is the spectrum of wheel graph. The results of this study show that steps in determining spectrum of detour matrix from the wheel graph with n+1 point Wn, that is: determine the wheel graph with n+1 point Wn; determine the detour; eigenvalues and eigenvectors of the wheel graph with n+1 point Wn; see the spectrum and patterns spectrum of detour matrix from the wheel graph with n+1 point Wn; pattern obtained in the form of conjecture then proved by formulating a theorem equipped with proof.Keywords: Spectrum, Detour Matrix, Wheel Graph.