共查询到20条相似文献,搜索用时 8 毫秒
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In this paper, a boundary value problem for a nonlinear second-order ordinary differential equation is studied. By means of the maximum principle we established the existence and the uniqueness of a solution of the problem. Then for finding the solution an iterative method is proposed. It is proved that this method converges much faster than the Picar successive approximations and in a particular case it gives two-sided monotone approximations to the exact solution of the problem. Finally, some illustrative examples are considered to confirm the efficiency of the method. 相似文献
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In this paper, the Adomian decomposition method is modified to solve a class of nonlinear singular boundary value problems which arise as nonlinear normal modal equations in nonlinear conservative vibratory systems. The effectiveness of the modified method is verified by three examples. 相似文献
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Fazhan Geng 《Applied mathematics and computation》2009,213(1):163-169
This paper presents a new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems. It is a relatively new analytical technique. The solution obtained by using the method takes the form of a convergent series with easily computable components. This paper will present a numerical comparison between our method and other methods for solving an open fourth-order boundary value problem presented by Scott and Watts. The method is also applied to a nonlinear fourth-order boundary value problem. The numerical results demonstrate that the new method is quite accurate and efficient for fourth-order boundary value problems. 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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Positive solutions of nonlinear singular third-order two-point boundary value problem 总被引:3,自引:0,他引:3
Shuhong Li 《Journal of Mathematical Analysis and Applications》2006,323(1):413-425
In this paper, we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problem
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An adaptive boundary element method for the exterior Stokes problem in three dimensions 总被引:2,自引:0,他引:2
** Email: vjervin{at}clemson.edu*** Email: norbert.heuer{at}brunel.ac.uk We present an adaptive refinement strategy for the h-versionof the boundary element method with weakly singular operatorson surfaces. The model problem deals with the exterior Stokesproblem, and thus considers vector functions. Our error indicatorsare computed by local projections onto 1D subspaces definedby mesh refinement. These indicators measure the error separatelyfor the vector components and allow for component-independentadaption. Assuming a saturation condition, the indicators giverise to an efficient and reliable error estimator. Also we describehow to deal with meshes containing quadrilaterals which arenot shape regular. The theoretical results are underlined bynumerical experiments. To justify the saturation assumption,in the Appendix we prove optimal lower a priori error estimatesfor edge singularities on uniform and graded meshes. 相似文献
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MoJiaqi LinWantao 《高校应用数学学报(英文版)》2005,20(2):159-164
The singularly perturbed boundary value problem for the nonlinear boundary conditions is considered. Under suitable conditions,the asymptotic behavior of solution for the original problems is studied by using theory of differential inequalities. 相似文献
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In this paper, we consider the pressure projection stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality problem of the second kind with the Stokes operator. The H1 and L2 error estimates for the velocity and the L2 error estimate for the pressure are obtained. Finally, the numerical results are displayed to verify the theoretical analysis. 相似文献
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In this paper, a novel method is proposed for solving nonlinear two-point boundary value problems (BVPs). This method is based on a combination of the Adomian decomposition method (ADM) and the reproducing kernel method (RKM). A major advantage of this method over standard ADM is that it can avoid unnecessary computation in determining the unknown parameters. The proposed method can be applied to singular and nonsingular BVPs. Numerical results obtained using the scheme presented here show that the numerical scheme is very effective and convenient for solving nonlinear two-point boundary value problems. 相似文献
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In this paper, we prove the existence and uniqueness of solutions for an anti-periodic boundary value problem of nonlinear impulsive differential equations of fractional order α∈(2,3] by applying some well-known fixed point theorems. Some examples are presented to illustrate the main results. 相似文献
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鲁世平 《高校应用数学学报(英文版)》2000,15(2):137-142
Abstract. In this paper,a kind of boundary value problems for Volterra functional differential e-quation is studied. 相似文献
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This paper investigates the existence of nontrivial solution for the three-point boundary value problem
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This paper is devoted to study the following third-order multi-point singularly perturbed boundary value problem
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Sergej Rjasanow 《Numerical Linear Algebra with Applications》1998,5(3):203-217
The algebraic properties of the matrix arising for the three-dimensional Dirichlet problem for Lamé equations in a rotational domain by the boundary element method are considered. The use of the special basis leads to a matrix having a block structure with sparse blocks. The possible strategies for the efficient solution of the above problem are discussed. © 1998 John Wiley & Sons, Ltd. 相似文献