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Some basic theorems of calculus on the field of p-adic numbers
Minggen Cui,정필웅,Huanping Liu 한국수학교육학회 2005 純粹 및 應用數學 Vol.12 No.2
In this paper, we introduce the concept of derivative of the function f : Qp ! R where Qp is the field of the p-adic numbers and R is the set of real numbers. And some basic theorems on derivatives are given.
SOLVING SINGULAR NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS IN THE REPRODUCING KERNEL SPACE
Geng, Fazhan,Cui, Minggen Korean Mathematical Society 2008 대한수학회지 Vol.45 No.3
In this paper, we present a new method for solving a nonlinear two-point boundary value problem with finitely many singularities. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation $u_n(x)$ to the exact solution u(x) is obtained and is proved to converge to the exact solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.
REPRODUCING KERNEL METHOD FOR SOLVING TENTH-ORDER BOUNDARY VALUE PROBLEMS
Geng, Fazhan,Cui, Minggen The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.3
In this paper, the tenth-order linear boundary value problems are solved using reproducing kernel method. The algorithm developed approximates the solutions, and their higher-order derivatives, of differential equations and it avoids the complexity provided by other numerical approaches. First a new reproducing kernel space is constructed to solve this class of tenth-order linear boundary value problems; then the approximate solutions of such problems are given in the form of series using the present method. Three examples compared with those considered by Siddiqi, Twizell and Akram [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345-362; S.S.Siddiqi, G.Akram, Solutions of tenth-order boundary value problems using eleventh degree spline, Applied Mathematics and Computation 185 (1)(2007) 115-127] show that the method developed in this paper is more efficient.
Solving singular nonlinear two-point boundary value problems in the reproducing kernel space
Fazhan Geng,Minggen Cui 대한수학회 2008 대한수학회지 Vol.45 No.3
In this paper, we present a new method for solving a nonlinear two-point boundary value problem with finitely many singularities. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation un(x) to the exact solution u(x) is obtained and is proved to converge to the exact solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other. In this paper, we present a new method for solving a nonlinear two-point boundary value problem with finitely many singularities. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation un(x) to the exact solution u(x) is obtained and is proved to converge to the exact solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.
REPRODUCING KERNEL METHOD FOR SOLVING TENTH-ORDER BOUNDARY VALUE PROBLEMS
Fazhan Geng,Minggen Cui 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.3
In this paper, the tenth-order linear boundary value problems are solved using reproducing kernel method. The algorithm developed ap-proximates the solutions, and their higher-order derivatives, of differential equations and it avoids the complexity provided by other numerical ap-proaches. First a new reproducing kernel space is constructed to solve this class of tenth-order linear boundary value problems; then the approximate solutions of such problems are given in the form of series using the present method. Three examples compared with those considered by Siddiqi, Twiz-ell and Akram [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345-362;S.S.Siddiqi, G.Akram, Solutions of tenth-order boundary value problems using eleventh degree spline , Applied Mathematics and Computation 185(1)(2007) 115-127] show that the method developed in this paper is more efficient.
NEW ALGORITHM FOR THE DETERMINATION OF ANUNKNOWN PARAMETER IN PARABOLIC EQUATIONS
Sufang Yue,Minggen Cui 한국수학교육학회 2008 純粹 및 應用數學 Vol.15 No.1
A new algorithm for the solution of an inverse problem of determining unknown source parameter in a parabolic equation in reproducing kernel space is considered. Numerical experiments are presented to demonstrate the accuracy and the e±ciency of the proposed algorithm.
Novel Method for Constructing New Wavelet Analysis
Yingzhen Lin,Minggen Cui 한국수학교육학회 2005 純粹 및 應用數學 Vol.12 No.4
In this paper, a new wavelet analysis of di��erential operator spline is generated, and it is of the symmetry and (3 ¡ ")-order regularity (0 < " < 3). Finally, using this wavelet basis, we expand Lebesgue square integrable functions e±ciently and quickly.