By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturb...By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.展开更多
Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly pertur...Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.展开更多
This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singula...This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations （ODEs） are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.展开更多
In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the met...In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.展开更多
基金Supported by the Innovation Talents of Science and Technology of Henan University(2009-HASTIT-007)Supported by the Natural Science Program of Department of Education(2011A110006)
文摘By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.
基金Project supported by the National Natural Science Foundation of China(Key Program)(Nos.11132004 and 51078145)
文摘Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.
基金supported by the National Natural Science Foundation of China(Key Program)(Nos.11132004 and 51078145)
文摘This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations （ODEs） are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.
基金supported by the National Natural Science Foundation of China (11132004 and 51078145)the Natural Science Foundation of Guangdong Province (9251064101000016)
文摘In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.
