New techniques for solving some matrix and matrix differential equations [PDF]
Ain Shams Engineering Journal, 2015 Matrix and matrix differential equations play an important role in system theory, control theory, stability theory of differential equations, communication systems and many other fields.
Zeyad Abdel Aziz Al-Zhour
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A New Operational Matrix of Fractional Derivatives to Solve Systems of Fractional Differential Equations via Legendre Wavelets [PDF]
Mathematics, 2018 This paper introduces a new numerical approach to solving a system of fractional differential equations (FDEs) using the Legendre wavelet operational matrix method (LWOMM).
Aydin Secer, Selvi Altun
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Solving a System of Sylvester-like Quaternion Matrix Equations [PDF]
Symmetry, 2022 Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary and sufficient solvability conditions for a system of Sylvester-type quaternion matrix equations, and give an expression of the general solution to the system when it is solvable.
Ruo-Nan Wang +2 more
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A system of dual quaternion matrix equations with its applications [PDF]
CoRR, 2023 We employ the M-P inverses and ranks of quaternion matrices to establish the necessary and sufficient conditions for solving a system of the dual quaternion matrix equations $(AX, XC) = (B, D)$, along with providing an expression for its general solution.
Lv-Ming Xie, Qing-Wen Wang 0001
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Numerical differential continuation approach for systems of nonlinear equations with singular Jacobian [PDF]
AUT Journal of Mathematics and Computing, 2022 It is well known that, one of the useful and rapid methods for a nonlinear system of algebraic equations is Newton’s method. Newton’s method has at least quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution ...
Mohammad Ali Mehrpouya
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Open Physics, 2022 Since obtaining an analytic solution to some mathematical and physical problems is often very difficult, academics in recent years have focused their efforts on treating these problems using numerical methods.
Ghamkhar Madiha +8 more
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Boundary value problems for matrix Euler-Poisson-Darboux equation with data on a characteristic
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2015 We consider the system of $n$ partial differential equations in matrix notation (the system of Euler-Poisson-Darboux equations). For the system we formulate the Cauchy-Goursat and Darboux problems for the case when the eigenvalues of the coefficient ...
Aleksander A Andreev +1 more
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On the Hermitian R‐Conjugate Solution of a System of Matrix Equations [PDF]
Journal of Applied Mathematics, 2012 Let R be an n by n nontrivial real symmetric involution matrix, that is, R = R−1 = RT ≠ In. An n × n complex matrix A is termed R‐conjugate if , where denotes the conjugate of A. We give necessary and sufficient conditions for the existence of the Hermitian R‐conjugate solution to the system of complex matrix equations AX = C and XB = D and present an
Chang-Zhou Dong +2 more
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Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations [PDF]
, 1991 Elsner L, Mehrmann V. Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations. Numerische Mathematik.
Mehrmann, Volker, Elsner, Ludwig
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Solution of Positive Periodic Discrete Lyapunov Equations with Applications to the Balancing of Periodic Systems. [PDF]
, 1997 The discrete-time positive periodic Lyapunov equations have important applications in the balancing and potentially also in the model reduction of discrete-time periodic systems.
A. Varga, Varga, A., Andreas Varga
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