Sorry, you do not have access to this eBook
A subscription is required to access the full text content of this book.
Metrics
Views
140
In This Chapter
-
Chapter 1: Methods for first-order differential equations
- GENERAL concepts. cauchy problem. Uniqueness and existence theorems
- Equations Solved for the Derivative. Simplest Techniques of lntegration *
- Equations with Separable Variables and Related Equations
- Homogeneous and Generalized Homogeneous Equations
- Linear Equation and Bernoulli Equation
- Darboux Equation and Other Equations
- Exact Differential Equations. lntegrating Factor
- Riccati Equation
- General riccati equation simplest integrable cases polynomial solutions
- Use of Particular Solutions to Construct the General Solution
- Some transformations
- Special Riccati Equation
- Abel Equations of the First Kind
- Abel Equations of the Second Kind
- General Form of Abel Equations of the Second Kind. Simplest Integrable Cases
- Some Transformations
- Use of Particular Solutions to Construct Self-Transformations and the General Solution
- Classification and Specific Features of Some CIasses of Solutions
- Stable and Unstable Solutions. Equilibrium Points
- BIow?Up Solutions
- Space Localization of Solutions
- Cauchy Problems Admitting Non?Unique Solutions
- Equations Not Solved for the Derivative and Equations Defined Parametrically
- Method of “Integration by Differentiation” for Equations Not Solved for the Derivative
- Equations Not Solved for the Derivative. Specific Equations
- Equations Defined Parametrically and Differential?AIgebraic Equations
- Contact Transformations
- General Form of Contact Transformations. Method for the Construction of Contact Transformations
- Examples of Contact Transformations
- Pfaffian equations
- Preliminary remarks
- Completely integrable pfaffian equations
- Pfaffian equations not satisfying the lntegrability condition
- Approximate analytic methods for solution of ODES
- Method of successive approximations (Picard Method)
- Newton–Kantorovich method
- Method of series expansion in the independent variable
- Method of regular expansion in the small parameter
- Differential inequalities and solution estimates
- Two theorems on solution estimates
- Chaplygin’s theorem and its applications (Bilateral Estimates of the Cauchy Problem Solution)
- Standard numerical methods for solving ordinary differential equations
- Singlestep methods. Runge–kutta methods
- Multistep methods
- Predictor–corrector methods
- Modified multistep methods (Butcher’s Methods)
- Stability and convergence of numerical methods
- Well and III $ {\text{III}} $ Conditioned Problems
- Special numerical methods for solving problems with qualitative features or singularities
Abstract
? Form of equations. General and particular solutions.
Other ways to access this content:
Email to request access
Purchase this book
Related chapters
Search for more...
© Informa UK Limited, an Informa Group Company
Home | About RHO | Collections
| Free trial
| How to buy
| Promotions
| Contact us | Help & FAQs
Librarian resources
| Privacy policy
| Cookies
| Terms & conditions
