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In This Chapter
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Chapter 7: Methods for nonlinear systems of ODES
- Solutions and first integrals. Uniqueness and existence theorems
- Systems solved for the derivative. A solution and the general solution
- Existence and uniqueness theorems
- Reduction of systems of equations to a single equation or to an autonomous system of equations
- First integrals. Using them to reduce system dimension
- Integrable combinations. Autonomous systems of equations
- Elements of stability theory
- Lyapunov stability. Asymptotic stability. Unstable solutions
- Theorems of stability and instability by first approximation
- Lyapunov function. Theorems of stability and instability
- Numerical integration
Abstract
We will be dealing with a system of first-order ordinary differential equations solved for the derivatives 7.1.1.1 y k ′ = f k ( x , y 1 , … , y n ) , k = 1 , . . . , n . $$ y^{\prime}_{k} = f_{k} (x,~y_{1} ,~ \ldots ,~y_{n} ),\,\,k = 1,...,n. $$
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