IMPROVED PRECISE DIRECT INTEGRATION METHOD FOR TIME-VARYING RICCATI DIFFERENTIAL EQUATION

Xiaomei Liu; Xiaolin Zhan; Xuanhao Zhang

doi:10.11948/20250250

2027 Volume 17 Issue 2

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Article navigation > Journal of Applied Analysis & Computation > 2027 > 17(2): 706-730

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Xiaomei Liu, Xiaolin Zhan, Xuanhao Zhang. IMPROVED PRECISE DIRECT INTEGRATION METHOD FOR TIME-VARYING RICCATI DIFFERENTIAL EQUATION[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 706-730. doi: 10.11948/20250250

Citation:

Xiaomei Liu, Xiaolin Zhan, Xuanhao Zhang. IMPROVED PRECISE DIRECT INTEGRATION METHOD FOR TIME-VARYING RICCATI DIFFERENTIAL EQUATION[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 706-730. doi: 10.11948/20250250

IMPROVED PRECISE DIRECT INTEGRATION METHOD FOR TIME-VARYING RICCATI DIFFERENTIAL EQUATION

1.
School of Mathematics, Physics and Statistics, Shanghai Polytechnic University, Shanghai 201209, China

Author Bio: Email: xlzhan@sspu.edu.cn(X. Zhan); Email: xhzhang@sspu.edu.cn(X. Zhang)
Corresponding author: Email: xmliu@sspu.edu.cn(X. Liu)

Abstract

Abstract

It is always limitations of existing approximate and numerical approaches to obtaining a high precision numerical solution of time-varying Riccati differential equation in a large region. A novel precise direct integration method (VHPD-TR) is proposed to compute the transfer matrix of the transformed differential equations from Riccati differential equation, instead of solving nonlinear algebraic equations. By introducing changes of variables and expanding dimensions, the Riccati equation is equivalently converted to a system of first-order time-varying differential equations, then approximately transformed into a time-invariant differential system, the solution of which is proved to converge to the exact solution of the Riccati differential equation as the expanding dimensions approach infinity. Moreover, the transformed time-invariant differential system can be precisely computed with the precise direct integration method even when the transfer matrix is stiff. The results of five examples verify the validity and simplicity of the proposed technique, and demonstrate the superior performance of VHPD-TR over previous methods.
- Riccati differential equation /
- precise direct integration method /
- time-varying system /
- stiff problem
MSC: 65L05, 65L04, 34A34

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References

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