Introduction to Singular Pεrturbation Theory1). Problem Statement Example: Quadratic equation \varepsilon x^2+2x-1=0 Truncate the perturbation series to O(\varepsilon^2): x(\varepsilon)=x_0+x_1\var…
A simple convection-diffusion problem is used as an example for a class of singular perturbation problems for which application of standard singular perturbation procedures could lead to misleading results. The properties of the operator appearing in the problem are identified and a solution technique ...
The use of finite-difference methods is considered for solving a singular perturbation problem for a linear ordinary differential equation with an interior... FW Dorr - 《Mathematics of Computation》 被引量: 33发表: 1971年 An example of ill-conditioning in the numerical solution of singular pertur...
For example, if we use some numerical method, the time and storage necessary for the solutions become less than originally possible. In this paper a singular perturbation problem, the existence and separation of the small, and large solutions of a differential equation is considered, but instead ...
asymptotic constants degenerate perturbation approximate correction singular ordinary illustrate explicitlyThis paper is taken up for the following difference equation problem(P,)(L,y)k≡εy(k+1)+a(k,ε)y(k)+b(k,ε)y(k-1)=f(k,ε)(1≤k≤N-1),B1y≡-y(0)+c1y(1)=a,B2y≡-c2y(...
The differential inequality theory has become an important means to deal with the singular perturbation boundary value problem. Its characteristic is that it can not only prove the existence of the solution of the perturbation problem, but also obtain an accurate estimation of the perturbation ...
perturbationapproximatecorrectionsingularordinaryillustrateexplicitly; , c,α,β constants and a(ε),b(ε),(ε)(1≤≤N) functions of and ε. Firstly, the case with constant coefficients is considered. Secondly, a general method based on extended transformation is given to handle (P) where the ...
High Gain Feedback Systems as Singular Singular-Perturbation Problems. As an example of a singular perturbation problem, we solve the high gain system dx/dt = A(t)x + B(t)u, u = gC(t)x as g = 1/mu goes to infinity. Our primary... R. E. O'Malley 被引量: 21发表: 1977年 ...
High Gain Feedback Systems as Singular Singular-Perturbation Problems. As an example of a singular perturbation problem, we solve the high gain system dx/dt = A(t)x + B(t)u, u = gC(t)x as g = 1/mu goes to infinity. Our primary... R. E. O'Malley 被引量: 21发表: 1977年 ...
An analysis by taking small values of the perturbation factors and by fixing the values of the FO derivatives is presented to solve the designed model. • Another analysis by using different FO derivatives values with fixed perturbation factor is provided for solving the LE model. • The desi...