The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . T...The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales .展开更多
To solve nonlinear system of equation,F(x) = 0,a continuous Newton flow x_t(t) = V(x) =-(DF(x))^(-1)F(x),x(0) =x^0 and its mathematical properties,such as the central field,global existence and uniqueness of real root...To solve nonlinear system of equation,F(x) = 0,a continuous Newton flow x_t(t) = V(x) =-(DF(x))^(-1)F(x),x(0) =x^0 and its mathematical properties,such as the central field,global existence and uniqueness of real roots and the structure of the singular surface,are studied.We concisely introduce random Newton flow algorithm(NFA) for finding all roots,based on discrete Newton flow x^(j+1)=x^j+hV{x^j) with random initial value x^0 and h∈(0,1],and three computable quantities,g_j,d_j and K_j.The numerical experiments with dimension n=300 are provided.展开更多
It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the genera...It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics,it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.展开更多
In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic ...In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method for avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given.展开更多
Nonlinear equations systems(NESs)arise in a wide range of domains.Solving NESs requires the algorithm to locate multiple roots simultaneously.To deal with NESs efficiently,this study presents an enhanced reinforcement...Nonlinear equations systems(NESs)arise in a wide range of domains.Solving NESs requires the algorithm to locate multiple roots simultaneously.To deal with NESs efficiently,this study presents an enhanced reinforcement learning based differential evolution with the following major characteristics:(1)the design of state function uses the information on the fitness alternation action;(2)different neighborhood sizes and mutation strategies are combined as optional actions;and(3)the unbalanced assignment method is adopted to change the reward value to select the optimal actions.To evaluate the performance of our approach,30 NESs test problems and 18 test instances with different features are selected as the test suite.The experimental results indicate that the proposed approach can improve the performance in solving NESs,and outperform several state-of-the-art methods.展开更多
文摘The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales .
基金National Natural Science Foundation of China(Grant Nos. 11301176,11071067 and 11226332)
文摘To solve nonlinear system of equation,F(x) = 0,a continuous Newton flow x_t(t) = V(x) =-(DF(x))^(-1)F(x),x(0) =x^0 and its mathematical properties,such as the central field,global existence and uniqueness of real roots and the structure of the singular surface,are studied.We concisely introduce random Newton flow algorithm(NFA) for finding all roots,based on discrete Newton flow x^(j+1)=x^j+hV{x^j) with random initial value x^0 and h∈(0,1],and three computable quantities,g_j,d_j and K_j.The numerical experiments with dimension n=300 are provided.
基金This work was supported by the National Natural Science Foundation of China (Grant No.10471128).
文摘It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics,it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.
基金The project was supported by the National Natural Science Faundation of China
文摘In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method for avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given.
基金This work was partly supported by the Natural Science Foundation of Guangxi Province(No.2020JJA170038)Special Talent Project of Guangxi Science and Technology Base(No.GuiKe AD21220119)the High-Level Talents Research Project of Beibu Gulf(No.2020KYQD06)。
文摘Nonlinear equations systems(NESs)arise in a wide range of domains.Solving NESs requires the algorithm to locate multiple roots simultaneously.To deal with NESs efficiently,this study presents an enhanced reinforcement learning based differential evolution with the following major characteristics:(1)the design of state function uses the information on the fitness alternation action;(2)different neighborhood sizes and mutation strategies are combined as optional actions;and(3)the unbalanced assignment method is adopted to change the reward value to select the optimal actions.To evaluate the performance of our approach,30 NESs test problems and 18 test instances with different features are selected as the test suite.The experimental results indicate that the proposed approach can improve the performance in solving NESs,and outperform several state-of-the-art methods.
