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Fast variable initial value search algorithm for control, prediction and numerical analysis

A technology of numerical analysis and search algorithm, applied in complex mathematical operations, etc., can solve undiscovered problems

Inactive Publication Date: 2008-12-03
BEIJING JIAOTONG UNIV
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

This kind of fast search algorithm for initial estimates of variables that does not depend on a priori has not been found in the specific problems of control, forecasting and numerical analysis of published literature research

Method used

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  • Fast variable initial value search algorithm for control, prediction and numerical analysis
  • Fast variable initial value search algorithm for control, prediction and numerical analysis
  • Fast variable initial value search algorithm for control, prediction and numerical analysis

Examples

Experimental program
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Effect test

Embodiment 1

[0023] figure 1 Plot of the output power of an Er-Yb co-doped short-cavity fiber laser as a function of fiber length calculated by the fast variable initial value search algorithm.

[0024] The calculation steps of the fast variable initial value search algorithm are:

[0025] Step 1, describe the nonlinear ordinary differential equations approximation model of the Erbium-Ytterbium co-doped short-cavity fiber laser, the independent variable is the reverse laser signal power, set the parameter K to 1, the divisor K1 to 2 and the absolute error limit of the numerical analysis results 10 -6 , the relative error limit of numerical analysis results is 10 -3 ;

[0026] Step 2, in the erbium-ytterbium co-doped short-cavity fiber laser, the power of the reverse laser signal is greater than 0 and less than the sum of the pump power coupled to the fiber laser, and the value range of the reverse laser signal power z=0 is the region [0 , Y max ], where Y max For the sum of the pumpi...

Embodiment 2

[0047] figure 2 Plot of forward laser signal power as a function of intracavity position for an exact model of nonlinear ordinary differential equations describing an ytterbium-doped fiber laser computed by the fast variable initial value search algorithm.

[0048] image 3 Plot of reverse laser signal power as a function of intracavity position for an exact model of nonlinear ordinary differential equations describing an ytterbium-doped fiber laser computed by the fast variable initial value search algorithm.

[0049] Figure 4 Plot of forward pump power as a function of intracavity position for an exact model describing nonlinear ordinary differential equations for an ytterbium-doped fiber laser, computed by the fast variable initial value search algorithm.

[0050] figure 2 , image 3 and Figure 4 The calculation steps of the fast variable initial value search algorithm used in are:

[0051] Step 1. In the exact model describing the nonlinear ordinary differential ...

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Abstract

The invention pertains to the control, forecasting and numerical analysis field, in particular to a fast variable initial value searching algorithm of a nonlinear ordinary differential equation set model. The algorithm needs not to carry out any setting to the variable initial estimation value, and only needs to carry out the initial limitation of the span of the variable initial estimation value according to the concrete problem of the control, forecasting and numerical analysis field and carry out initial setting to the condition of convergency of the nonlinear ordinary differential equation set model describing the concrete problem of the control, forecasting and numerical analysis field, therefore, the nonlinear ordinary differential equation set model describing the concrete problem of the control, forecasting and numerical analysis field can automatically, stably and rapidly obtain the correct numerical solving result meeting given accuracy requirements and find out the independent variable initial estimation value of the correct numerical solving result, which causes the nonlinear ordinary differential equation set model to be converged to the given accuracy requirements.

Description

technical field [0001] The invention belongs to the fields of control, forecast and numerical analysis, and is specifically a fast variable initial value search algorithm for a nonlinear ordinary differential equation model. Background technique [0002] Degree theory and related fixed point theorems [Ge Weigao. Boundary value problems for nonlinear ordinary differential equations. Beijing: Science Press 2007pp39-68] are basic tools for studying boundary value problems for nonlinear ordinary differential equations. However, the analysis process is very complicated. Mathematical theory requires high requirements, and complex forms of analytical solutions or semi-analytic solutions are often obtained, which is not conducive to numerical analysis. With the increase of the number of variables, it will be very difficult to obtain the analytical solution of the nonlinear ordinary differential equation boundary value problem. The shooting method [Robert J. Schilling (Robert J. Schi...

Claims

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Application Information

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IPC IPC(8): G06F17/13
Inventor 胡旭东宁提纲陈青艳裴丽阮乂祁春慧郑晶晶
Owner BEIJING JIAOTONG UNIV
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