An equation that has two or more independent variables, an unknown function that depends on those variables, and partial derivatives of the unknown function with respect to the independent variables is known as a partial differential equation (or PDE for short). The largest derivative included determines the partial differential equation's order. A partial differential equation's solution (or a specific solution) is a function that, when substituted into the equation, solves the partial differential equation or, to put it another way, converts it into an identity. If a solution encompasses each unique solution to the problem in question, it is referred to as a generic solution.

The mathematical formulation of physical and other issues requiring functions of several variables, such as the transmission of heat or sound, fluid flow, elasticity, electrostatics, electrodynamics, etc., is facilitated by the use of partial differential equations. Any function that satisfies a partial differential equation exactly is said to be its solution. Any solution that has a number of arbitrary independent functions equal to the order of the equation is said to be a general solution. A specific solution is one that is produced by a specific set of arbitrary functions and is derivable from the general solution. By selecting a specific set of random functions, a unique solution is one that cannot be deduced from the general solution.

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

1. Review of partial differential equations
2. Elliptical equations with relevant examples
3. Parabolic equations with relevant examples
4. Hyperbolic equations with relevant examples

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The article Solution of Partial Differential Equations - Numerical Methods is contributed by Namrata Chaudhary, a student of Lumbini Engineering College (LEC).

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