共查询到20条相似文献,搜索用时 9 毫秒
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The article considers the determination of the solution-dependent coefficient of a nonautonomous ordinary differetial equation
with a parameter. Reduction of the inverse problem to a nonlinear operator equation is used to prove existence and uniqueness
theorems and to propose an iterative solution method.
Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 5–17. 相似文献
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V. P. Tanana 《Numerical Analysis and Applications》2010,3(4):367-380
An order-optimal method is developed to solve an inverse problem for a parabolic heat conduction equation with a variable coefficient. 相似文献
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M. Sh. Burlutskaya A. P. Khromov 《Computational Mathematics and Mathematical Physics》2011,51(12):2102-2114
The Fourier method is used to obtain a classical solution of an initial-boundary value problem for a first-order partial differential
equation with involution in the function and its derivative. The series Σ produced by the Fourier method as a formal solution
of the problem is represented as Σ = S
0 + (Σ − Σ0), where Σ0 is the formal solution of a special reference problem for which the sum S
0 can be explicitly calculated. Refined asymptotic formulas for the solution of the Dirac system are used to show that the
series Σ − Σ0 and the series obtained from it by termwise differentiation converge uniformly. Minimal smoothness assumptions are imposed
on the initial data of the problem. 相似文献
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V. P. Tanana 《Journal of Applied and Industrial Mathematics》2009,3(3):395-400
An order-optimal method is proposed of approximately solving an inverse problem for a parabolic equation with variable coefficients.
We give an order-exact estimate for the error of the method. 相似文献
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A coefficient inverse problem of the one-dimensional parabolic equation is solved by a high-order compact finite difference method in this paper. The problem of recovering a time-dependent coefficient in a parabolic partial differential equation has attracted considerable attention recently. While many theoretical results regarding the existence and uniqueness of the solution are obtained, the development of efficient and accurate numerical methods is still far from satisfactory. In this paper a fourth-order efficient numerical method is proposed to calculate the function u(x,t) and the unknown coefficient a(t) in a parabolic partial differential equation. Several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method. 相似文献
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《Journal of Computational and Applied Mathematics》2002,147(1):153-173
A parameter identification problem for the hydraulic properties of porous media is considered. Numerically, this inverse problem is solved by minimizing an output least-squares functional. The unknown hydraulic properties which are nonlinear coefficients of a partial differential equation are approximated by spline functions. The identification is embedded into a multi-level algorithm and coupled with a linear sensitivity analysis to describe the ill-posedness of the inverse problem. 相似文献
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V. B. Dmitriev 《Russian Mathematics (Iz VUZ)》2012,56(4):1-8
In this paper we study a nonlocal problem for a first-order partial differential equation with an integral condition instead
of the standard boundary one. We prove that the problem under consideration is uniquely solvable. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(6):2421-2437
Using the solutions of an auxiliary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some Wick-type nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained. In addition, the links between Wick-type partial differential equations and variable coefficient partial differential equations are also clarified generally. 相似文献
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A. M. Denisov 《Differential Equations》2017,53(7):916-922
For a hyperbolic equation, we consider an inverse coefficient problem in which the unknown coefficient occurs in both the equation and the initial condition. The solution values on a given curve serve as additional information for determining the unknown coefficient. We suggest an iterative method for solving the inverse problem based on reduction to a nonlinear operator equation for the unknown coefficient and prove the uniform convergence of the iterations to a function that is a solution of the inverse problem. 相似文献
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Lazhar Bougoffa 《Journal of Applied Mathematics and Computing》2013,43(1-2):31-54
In this paper, we present a new approach to solve nonlocal initial-boundary value problems of linear and nonlinear hyperbolic partial differential equations of first-order subject to initial and nonlocal boundary conditions of integral type. We first transform the given nonlocal initial-boundary value problems into local initial-boundary value problems. Then we apply a modified Adomian decomposition method, which permits convenient resolution of these problems. Moreover, we prove this decomposition scheme applied to such nonlocal problems is convergent in a suitable Hilbert space, and then extend our discussion to include systems of first-order linear equations and other related nonlocal initial-boundary value problems. 相似文献
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Yu. E. Anikonov 《Mathematical Notes》1972,12(2):533-535
An inverse problem is solved for an ordinary second-order differential equation.Translated from Matematicheskie Zametki, Vol. 12, No. 2, pp. 163–166, August, 1972. 相似文献
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The Fourier method is used to find a classical solution of the mixed problem for a first-order differential equation with involution and periodic boundary conditions. The application of the Fourier method is substantiated using refined asymptotic formulas obtained for the eigenvalues and eigenfunctions of the corresponding spectral problem. The Fourier series representing the formal solution is transformed using certain techniques, and the possibility of its term-by-term differentiation is proved. Minimal requirements are imposed on the initial data of the problem. 相似文献
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Dulat Dzhumabaev Elmira Bakirova Sandugash Mynbayeva 《Mathematical Methods in the Applied Sciences》2020,43(4):1788-1802
A nonlinear loaded differential equation with a parameter on a finite interval is studied. The interval is partitioned by the load points, at which the values of the solution to the equation are set as additional parameters. A nonlinear boundary value problem for the considered equation is reduced to a nonlinear multipoint boundary value problem for the system of nonlinear ordinary differential equations with parameters. For fixed parameters, we obtain the Cauchy problems for ordinary differential equations on the subintervals. Substituting the values of the solutions to these problems into the boundary condition and continuity conditions at the partition points, we compose a system of nonlinear algebraic equations in parameters. A method of solving the boundary value problem with a parameter is proposed. The method is based on finding the solution to the system of nonlinear algebraic equations composed. 相似文献
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An iterative method for finding a solution of the equation f(x)=0 is presented. The method is based on some specially derived quadrature rules. It is shown that the method can give better results than the Newton method. 相似文献