This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theo...This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theorem,fixed point index theory and the analytic technique,we give the bifurcation point of the parameter which divides the range of parameter for the existence of at least two,one and no positive solutions for the problem.And,by using a fixed point theorem of generalized concave operator and cone theory,we establish the maximum parameter interval for the existence of the unique positive solution for the problem and show that such a positive solution continuously depends on the parameter.In the end,some examples are given to illustrate our main results.展开更多
This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit...This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.展开更多
With the evolution of geophysical surveys from traditional two-dimensional(2 D)to three-dimensional(3 D)models,the resulting large data volumes pose significant challenges to inversion,particularly when resolving larg...With the evolution of geophysical surveys from traditional two-dimensional(2 D)to three-dimensional(3 D)models,the resulting large data volumes pose significant challenges to inversion,particularly when resolving large-scale 3 D structures.A direct solver for solving an ill-conditioned linear system resulting from the finite-difference approximation of a boundary value problem requires more memory and time than iterative solvers.To overcome this limitation,an efficient iterative solver for 3 D finite-difference approach is introduced to calculate the 3 D gravitational potential and the associated gravitational field.Firstly,the boundary value problem associated with 3 D gravitational potential is discretized using central finite-difference technique based on right rectangular prismatic grids.The resulting large unsymmetric sparse systems are then solved using the generalized minimal residual algorithm(GMRES)iterative solver in combination with incomplete LU factorization.Secondly,to obtain high-accuracy partial derivatives of gravitational potential,a high-degree Lagrange interpolation scheme is employed.Finally,three density models are applied to test the accuracy,reliability,and flexibility of our 3 D finite-difference algorithm.All computational results demonstrate that our method provides an accurate approximation of the gravitational field and is applicable to 3 D forward modeling.展开更多
The conversion theory of vector wave function is one of important problems in electromagnetic. This paper presents a systematic treatment of the conversion technique and some applications. In this paper, the conversio...The conversion theory of vector wave function is one of important problems in electromagnetic. This paper presents a systematic treatment of the conversion technique and some applications. In this paper, the conversion relations of standard and non-standard spherical vector wave functions, standard and non-standard cylindrical vector wave functions, and spherical and cylindrical vector wave functions are developed. As an example of application of vector wave function expansion, the expansion of plane wave and dipole field in two-medium half-spaces are given. As an example of application of vector wave function conversion, the scattering patterns of buried conducting and dielectric spheres are presented. Inspection on the numerical results shows that the technique and associated programs presented in this paper are efficient.展开更多
In this paper, a rather general class of explicit parallel multistep Runge-Kutta methods is constructed for solving initial value problem of ordinary differential equations. Also, the corresponding convergence and sta...In this paper, a rather general class of explicit parallel multistep Runge-Kutta methods is constructed for solving initial value problem of ordinary differential equations. Also, the corresponding convergence and stability are analysed. Several parallel computational formulae are given. The numerical experiments, including accuracy, speedup, and efficiency tests show that the methods are efficient.展开更多
基金Supported by the National Natural Science Foundation of China(11361047)Fundamental Research Program of Shanxi Province(20210302124529)。
文摘This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theorem,fixed point index theory and the analytic technique,we give the bifurcation point of the parameter which divides the range of parameter for the existence of at least two,one and no positive solutions for the problem.And,by using a fixed point theorem of generalized concave operator and cone theory,we establish the maximum parameter interval for the existence of the unique positive solution for the problem and show that such a positive solution continuously depends on the parameter.In the end,some examples are given to illustrate our main results.
文摘This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.
基金Project(2025ZD1009704)supported by the National Science and Technology Major Project of ChinaProjects(2023JJ30659,2022JJ30706)supported by Hunan Provincial Natural Science Foundation,China。
文摘With the evolution of geophysical surveys from traditional two-dimensional(2 D)to three-dimensional(3 D)models,the resulting large data volumes pose significant challenges to inversion,particularly when resolving large-scale 3 D structures.A direct solver for solving an ill-conditioned linear system resulting from the finite-difference approximation of a boundary value problem requires more memory and time than iterative solvers.To overcome this limitation,an efficient iterative solver for 3 D finite-difference approach is introduced to calculate the 3 D gravitational potential and the associated gravitational field.Firstly,the boundary value problem associated with 3 D gravitational potential is discretized using central finite-difference technique based on right rectangular prismatic grids.The resulting large unsymmetric sparse systems are then solved using the generalized minimal residual algorithm(GMRES)iterative solver in combination with incomplete LU factorization.Secondly,to obtain high-accuracy partial derivatives of gravitational potential,a high-degree Lagrange interpolation scheme is employed.Finally,three density models are applied to test the accuracy,reliability,and flexibility of our 3 D finite-difference algorithm.All computational results demonstrate that our method provides an accurate approximation of the gravitational field and is applicable to 3 D forward modeling.
文摘The conversion theory of vector wave function is one of important problems in electromagnetic. This paper presents a systematic treatment of the conversion technique and some applications. In this paper, the conversion relations of standard and non-standard spherical vector wave functions, standard and non-standard cylindrical vector wave functions, and spherical and cylindrical vector wave functions are developed. As an example of application of vector wave function expansion, the expansion of plane wave and dipole field in two-medium half-spaces are given. As an example of application of vector wave function conversion, the scattering patterns of buried conducting and dielectric spheres are presented. Inspection on the numerical results shows that the technique and associated programs presented in this paper are efficient.
文摘In this paper, a rather general class of explicit parallel multistep Runge-Kutta methods is constructed for solving initial value problem of ordinary differential equations. Also, the corresponding convergence and stability are analysed. Several parallel computational formulae are given. The numerical experiments, including accuracy, speedup, and efficiency tests show that the methods are efficient.
