Numerical Simulation of One-Dimensional Fractional Nonsteady Heat Transfer Model Based on the Second Kind Chebyshev Wavelet by Fuqiang Zhao, Jiaquan Xie, Qingxue Huang

“…The operational matrix of fractional-order integration is utilized to reduce the original problem to a system of linear algebraic equations, and then the numerical solutions obtained by our method are compared with those obtained by CAS wavelet method. …”
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Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations by Şuayip Yüzbaşı, Mehmet Sezer

“…By aid of the collocation points and the matrix operations, the suggested scheme converts singularly perturbed problem into a matrix equation, and this matrix equation corresponds to a system of linear algebraic equations. Also, an error analysis technique based on the residual function is introduced for the method. …”
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Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactifications by Linh, Nguyen Manh

“…We show that this inclusion is not always an isomorphism, even in the case where $X$ is a homogeneous space of a connected linear algebraic group over $K$. A similar result for the smooth compactifications of $X$ is also given.…”
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Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes by G. E. Okecha

“…The problem is reduced to a system of linear algebraic equations. A theoretical convergence result for the approximation is provided. …”
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Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs by A. Pirkhedri, H. H. S. Javadi, H. R. Navidi

“…This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. …”
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SIMULATION OF THE ELECTROSTATIC DIPOLE FIELD IN THE PRESENCE OF A THIN UNCLOSED OBLATE ELLIPSOIDAL SHELL AND PLANE by G. Ch. Shushkevich

“…Using the addition theorems connecting spherical, ellipsoidal and cylindrical harmonic functions, the solution of the boundary problem is reduced to the solution of dual series equations by the Legendre polynomials that are transformed to an infinite system of linear algebraic equations of the second kind with a completely continuous operator. …”
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Finite-part singular integral approximations in Hilbert spaces by E. G. Ladopoulos, G. Tsamasphyros, V. A. Zisis

“…Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several systems of linear algebraic equations. The method is further extended for the proof of the existence of solutions for systems of finite-part singular integral equations defined on Hilbert spaces, when their singularity consists of a system of diffeomorphisms of the integration interval, which is a unit circle, on itself.…”
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The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation by Lu-feng Yang

“…By the Laplace transform, the ordinary differential equation about the orthogonal expansion coefficient is transformed into a linear algebraic equation system, with the coefficient matrix being a tridiagonal lower triangular matrix. …”
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A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain by Faezeh Toutounian, Emran Tohidi, Stanford Shateyi

“…This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown Bernoulli coefficients are determined and thus the approximate solutions are obtained. …”
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ANALYTICAL STUDY OF THE STATIC THERMOMECHANICAL STRESSES OF THE ASSEMBLIES WITH OPTIONAL RING FLANGES. ROTATION OF THE FLANGE RING AROUND THE CIRCUMFERENCE OF CENTERS FOR BOLT HOLE... by IATAN RADU I., GHEORGHITA TOMESCU, GEORGETA ROMAN (URSE), MELANIA CORLECIUC (MITUCA), IOLANDA CONSTANTA PANAIT

“…Regarding of the above, the compatibility of the deformations of the component elements (radial displacements and rotations) is approached. A linear algebraic system is formed in which both external loads (pressure, temperature) and connecting loads (bending unit moments and unit forces) are present. …”
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Numerical Solution for the 2D Linear Fredholm Functional Integral Equations by Neda Khaksari, Mahmoud Paripour, Nasrin Karamikabir

“…Using the proposed method, we get a system of linear algebraic equations which are solved by an iteration method. …”
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Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method by Fengying Zhou, Xiaoyong Xu

“…Based on the collocation technique, the second-kind Chebyshev wavelets are used to reduce the problem to the solution of a system of linear algebraic equations. Several examples are provided to confirm the reliability and effectiveness of the proposed method.…”
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Finite difference solution of radiation effects on MHD unsteady free-convection flow over vertical plate with variable surface temperature by M. A. Abd El-Naby, Elsayed M. E. Elbarbary, Nader Y. Abdelazem

“…The boundary layer equations are transformed into a linear algebraic system by an implicit finite-difference method. …”
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Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions by Bashar Zogheib, Emran Tohidi, Stanford Shateyi

“…., CGL collocation points), equations will be transformed into the associated systems of linear algebraic equations which can be solved by robust Krylov subspace iterative methods such as GMRES. …”
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Topology in nonlinear extensions of hypernumbers by M. S. Burgin

“…In this paper, nonlinear structures are introduced in spaces of real and complex hypernumbers by extending the concept of a hypernumber. In such a way, linear algebras of extended hypernumbers are built. A special topology of conical neighborhoods in these algebras is introduced and studied. …”
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Construction Solutions of PDE in Parametric Form by Alexandra K. Volosova, Konstantin Alexandrovich Volosov

“…In the case of two independent variables 𝑥,𝑡, then it always gives the possibility of expressing all PDE second and more order as 𝐴𝑋=𝑏. This is a linear algebraic equations system with regards derivatives to old variables 𝑥(𝜉,𝛿), 𝑡(𝜉,𝛿) on new variables 𝜉,𝛿∶(𝑥′𝜉,𝑥′𝛿,𝑡′𝜉,𝑡′𝛿). …”
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Numerical method for solving the subdiffusion differential equation with nonlocal boundary conditions by Murat A. Sultanov, Vladimir E. Misilov, Makhmud A. Sadybekov

“…The Thomas algorithm was used to solve systems of linear algebraic equations. Numerical experiments were conducted to study the constructed algorithm. …”
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A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems by Yidu Yang, Wei Jiang, Yu Zhang, Wenjun Wang, Hai Bi

“…With this scheme, the solution of an eigenvalue problem on a fine grid Kh is reduced to the solution of an eigenvalue problem on a much coarser grid KH and the solution of a linear algebraic system on the fine grid Kh. Theoretical analysis shows that the scheme has high efficiency. …”
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Method of formation of numerical projection-grid algorithm on basis of «three-dimensional regular element» for calculation of 3D-models of magnetic field in cylindrical coordinate... by A. A. Tatevosyan, E. G. Andreeva

“…The use of the «three-dimensional regular element» makes it possible to automate the process of forming a global system of linear algebraic equations in the projection-grid Galerkin method in combination with the finite element method bypassing the stage of constructing elemental systems of equations. …”
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Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System by Ghazwa F. Abd, Radhi A. Zaboon

“…The unknown coefficients of the solution are obtained by solving a linear algebraic system. The different index problems of linear Hessenberg differential-algebraic control systems are approximately solved using this approach with comparisons. …”
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