Boundary value problems for second order singularly perturbed differential equations

1988 ◽  
Vol 9 (1) ◽  
pp. 95-99 ◽  
Author(s):  
Zhou Qin-de ◽  
Miao Shu-mei
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Singularly Perturbed

scholarly journals SOLVING BOUNDARY VALUE PROBLEMS FOR SECOND ORDER SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS BY Ε-APPROXIMATE FIXED-POINT METHOD

2015 ◽  
Vol 20 (3) ◽  
pp. 369-381 ◽  
Author(s):  
Zbigniew Bartoszewski ◽  
Anna Baranowska
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Delay Differential Equations ◽  
Boundary Value ◽  
Cubic Spline ◽  
Second Order ◽  
Singularly Perturbed ◽  
Grid Points ◽  
Delay Differential

In this paper, the boundary value problem for second order singularly perturbed delay differential equation is reduced to a fixed-point problem v = Av with a properly chosen (generally nonlinear) operator A. The unknown fixed-point v is approximated by cubic spline v h defined by its values v i = v h (t i ) at grid points t i , i = 0, 1, . . . , N. The necessary for construction the cubic spline and missing the first derivatives at the boundary are replaced by the derivatives of the corresponding interpolating polynomials matching the grid points values nearest to the boundary points. An approximation of the solution is obtained by minimization techniques applied to a function whose arguments are the grid point values of the sought spline. The results of numerical experiments with two boundary value problems for the second order singularly perturbed delay differential equations as well as their comparison with the results of other methods employed by other authors are also provided.

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