In this paper,we consider the system of Sturm-Liouville singular BVP and present a sufficient and necessary condition for the existence of positive solutions by means of the fixed point theorem for regular cones.
In this article, we establish the existence of positive solution for the following Hadamard fractional singular boundary value problem where is continuous and singular at t = a, t = b and x = 0. Further, is Hada...In this article, we establish the existence of positive solution for the following Hadamard fractional singular boundary value problem where is continuous and singular at t = a, t = b and x = 0. Further, is Hadamard fractional derivative of order μ. Moreover, the existence of positive solution has been established using fixed point index for a completely continuous map in a cone. Also, an example is included to show the validity of our result.展开更多
In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u...In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u)0. n is positive integer and n2. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution.展开更多
<div style="text-align:justify;"> In this paper, the numerical solution and its error analysis of quasilinear singular perturbation two-point boundary value problems based on the principle of equidistr...<div style="text-align:justify;"> In this paper, the numerical solution and its error analysis of quasilinear singular perturbation two-point boundary value problems based on the principle of equidistribution are given. On the non-uniform grid of the uniformly distributed arc-length monitor function, the solution of the simple upwind scheme is obtained. It is proved that the adaptive simple upwind scheme based on the principle of equidistribution has uniform convergence for small perturbation parameters. Numerical experiments are carried out and the error analysis are confirmed. </div>展开更多
A singularly perturbed advection-diffusion two-point Robin boundary value problem whose solution has a single boundary layer is considered. Based on the piecewise linear polynomial approximation, the finite element me...A singularly perturbed advection-diffusion two-point Robin boundary value problem whose solution has a single boundary layer is considered. Based on the piecewise linear polynomial approximation, the finite element method is applied to the problem. Estimation of the error between solution and the finite element approximation is given in energy norm on shishkin-type mesh.展开更多
基金supported by the NSF of Shandong Province (No.2010AL013)
文摘In this paper,we consider the system of Sturm-Liouville singular BVP and present a sufficient and necessary condition for the existence of positive solutions by means of the fixed point theorem for regular cones.
文摘In this article, we establish the existence of positive solution for the following Hadamard fractional singular boundary value problem where is continuous and singular at t = a, t = b and x = 0. Further, is Hadamard fractional derivative of order μ. Moreover, the existence of positive solution has been established using fixed point index for a completely continuous map in a cone. Also, an example is included to show the validity of our result.
文摘In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u)0. n is positive integer and n2. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution.
文摘<div style="text-align:justify;"> In this paper, the numerical solution and its error analysis of quasilinear singular perturbation two-point boundary value problems based on the principle of equidistribution are given. On the non-uniform grid of the uniformly distributed arc-length monitor function, the solution of the simple upwind scheme is obtained. It is proved that the adaptive simple upwind scheme based on the principle of equidistribution has uniform convergence for small perturbation parameters. Numerical experiments are carried out and the error analysis are confirmed. </div>
文摘A singularly perturbed advection-diffusion two-point Robin boundary value problem whose solution has a single boundary layer is considered. Based on the piecewise linear polynomial approximation, the finite element method is applied to the problem. Estimation of the error between solution and the finite element approximation is given in energy norm on shishkin-type mesh.
