Fundamental Solution of Elliptic Equation with Positive Definite Matrix Coefficient [PDF]
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2018 In this paper, we study the fundamental solution of elliptic equations with real constant coefficients where is a positive definite matrix. We obtained by searching the radial solution so that we solved the equation into ordinary differential equations.
Khoirunisa Khoirunisa, Corina Karim
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Solution of heat equation by a novel implicit scheme using block hybrid preconditioning of the conjugate gradient method [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 The main goal of the study is the approximation of the solution to the Dirichlet boundary value problem (DBVP) of the heat equation on a rectangle by developing a new difference method on a grid system of hexagons.
S.C. Buranay, N. Arshad
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Best Proximity Point and Existence of the Positive Definite Solution for Matrix Equations
International Journal of Analysis and Applications, 2023 In this research, α − ψ − θ contraction has been defined to find the best proximity point in partially ordered metric spaces. Proper support for the result has been given in the form of a suitable example.
Satyendra Kumar Jain +2 more
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Fundamental solution of fractional Kolmogorov–Fokker–Planck equation
Examples and Counterexamples, 2021 In this paper, we construct an explicit fundamental solution for the fractional Kolmogorov–Fokker–Planck equation. To achieve this goal, the Fourier transform is applied, and the method of characteristics and the properties of positive definite matrix ...
Cong He +3 more
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Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations
Journal of Mathematics, 2021 In this work, the following system of nonlinear matrix equations is considered, X1+A∗X1−1A+B∗X2−1B=I and X2+C∗X2−1C+D∗X1−1D=I, where A,B,C, and D are arbitrary n×n matrices and I is the identity matrix of order n.
Sourav Shil, Hemant Kumar Nashine
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Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q (p>0)
Abstract and Applied Analysis, 2013 The nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated.
Jing Li
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CG Versus MINRES: An Empirical Comparison
Sultan Qaboos University Journal for Science, 2012 For iterative solution of symmetric systems the conjugate gradient method (CG) is commonly used when A is positive definite, while the minimum residual method (MINRES) is typically reserved for indefinite systems.
David Chin-Lung Fong, Michael Saunders
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Implicit Approximation Scheme for the Solution of K-Positive Definite Operator Equation
Abstract and Applied Analysis, 2014 We construct an implicit sequence suitable for the approximation of solutions of K-positive definite operator equations in real Banach spaces. Furthermore, implicit error estimate is obtained and the convergence is shown to be faster in comparsion to the
Naseer Shahzad, Arif Rafiq, Habtu Zegeye
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On the Solution of the Rational Matrix Equation X=Q+LX−1LT
EURASIP Journal on Advances in Signal Processing, 2007 We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation X=Q+LX−1LT, where Q is symmetric positive definite and L is nonsingular.
Heike Faßbender, Peter Benner
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Stability of solutions and the problem of Aizerman for sixth-order differential equations
Журнал Белорусского государственного университета: Математика, информатика, 2020 This article is devoted to the investigation of stability of equilibrium of ordinary differential equations using the method of semi-definite Lyapunov’s functions.
Boris S. Kalitine
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