Unit V: Solution of Ordinary Differential Equations | BCA 4th Semester Numerical Methods Notes Pdf

In mathematics, an ordinary differential equation (also known as an ODE) is an equation made up of one or more functions of a single independent variable and its derivatives. A function having one or more derivatives is a component of a differential equation. However, when referring to the derivative of a function for a single independent variable in an ODE, the word "ordinary" is used.

Ordinary differential equations (ODEs) are a common occurrence in the social, natural, and mathematical sciences. Differentials and derivatives are used in mathematical representations of change. Differential equations, which explain dynamically changing events, evolution, and variation, are created when various differentials, derivatives, and functions are coupled by equations. Quantities frequently enter differential equations as gradients of quantities or as the rate of change of other quantities (for instance, derivatives of displacement with respect to time). Geometry and analytical mechanics are examples of specific mathematical disciplines. A large portion of physics, astronomy, meteorology, chemistry, biology, ecology, population modeling, and economics are considered scientific areas.

In this “Solution of Ordinary Differential Equations - Numerical Methods” you will learn about the following topics:

1. Overview of initial and boundary value problems
2. The Taylor’s series method
3. The Euler Method and its modifications
4. Huen’s methods
5. Runge Kutta methods
6. Solution of higher-order equations
7. Boundary Value problems: Shooting method

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BCA 4th Semester Numerical Methods Notes Pdf:

• Unit I: Solution of Nonlinear Equations
• Unit II: Interpolation and Approximation
• Unit III: Numerical Differentiation and Integration
• Unit IV: Solution of Linear Algebraic Equations
• Unit VI: Solution of Partial Differential Equations