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On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method
Published 2021-01-01“…In this study, we investigate the semianalytic solution of the fifth-order Kawahara partial differential equation (KPDE) with the approach of fractional-order derivative. …”
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Research on Image Recognition of Building Wall Design Defects Based on Partial Differential Equation
Published 2021-01-01“…Then, the improved partial differential equation is used to recognize the image as a whole. …”
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Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition
Published 2012-01-01“…The numerical and analytic solutions of the mixed problem for multidimensional fractional hyperbolic partial differential equations with the Neumann condition are presented. …”
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The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface
Published 2015-01-01“…We investigate properties of algorithms that are used to solve coupled evolutionary partial differential equations posed on neighboring, nonoverlapping domains, where the solutions are coupled by continuity of state and normal flux through a shared boundary. …”
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An experimental comparison of two preconditioned iterative methods to solve the elliptic partial differential equations
Published 2022-03-01Subjects: Get full text
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Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
Published 2013-01-01“…A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs). The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs). …”
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An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions
Published 2014-01-01“…One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs) as well as PDEs with variable coefficients. …”
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Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations
Published 2015-01-01“…Meshless method of line is a powerful device to solve time-dependent partial differential equations. In integrating step, choosing a suitable set of points, such as adaptive nodes in spatial domain, can be useful, although in some cases this can cause ill-conditioning. …”
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Some maximum principles for solutions of a class of partial differential equations in Ω⊂ℝn
Published 2000-01-01“…We find maximum principles for solutions of semilinear elliptic partial differential equations of the forms: (1) Δ2u+αf(u)=0, α∈ℝ+ and (2) ΔΔu+α(Δu)k+gu=0, α≤0 in some region Ω⊂ℝn.…”
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A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations
Published 2016-01-01“…Exact solution of linear and nonlinear fractional partial differential equations is successfully obtained using the analytical method.…”
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On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations
Published 2014-01-01“…This paper presents a new application of the homotopy analysis method (HAM) for solving evolution equations described in terms of nonlinear partial differential equations (PDEs). The new approach, termed bivariate spectral homotopy analysis method (BISHAM), is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. …”
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Barcode Location in Financial Statement System Based on the Partial Differential Equation Image Recognition Algorithm
Published 2021-01-01“…This paper studies the problem of the barcode image location and recognition in the financial statement system and tries to apply the partial differential equation image recognition algorithm to the barcode location in the financial statement system. …”
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Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications
Published 2020-01-01“…In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and complex geometries. …”
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Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations
Published 2014-01-01“…A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. …”
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On the Coupling of the Homotopy Perturbation Method and New Integral Transform for Solving Systems of Partial Differential Equations
Published 2019-01-01“…This combination allows to obtain analytic and numerical solutions for linear and nonlinear systems of partial differential equations.…”
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Existence Results for a Class of Semilinear Fractional Partial Differential Equations with Delay in Banach Spaces
Published 2019-01-01“…In this paper, we consider a class of nonlinear time fractional partial differential equations with delay. We obtain the existence and uniqueness of the mild solutions for the problem by the theory of solution operator and the general Banach contraction mapping principle. …”
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