MATLAB is a multi-paradigm
numerical computing environment and fourth-generation programming language. A
proprietary language developed by MathWorks, MATLAB allows matrix
manipulations, plotting of functions and data, implementation of algorithms, a
creation of user interfaces, and interfacing with programs written in other
languages, including C, C++, Java, Fortran and Python. An additional package,
Simulink, adds graphical multi-domain simulation and model-based design for
dynamic and embedded systems. MATLAB is also used for simulation of ODE/PDE
ODE/PDE in MATLAB toolbox
Matlab makes use of many toolboxes each catering to a specific area. Partial Differential Equation Toolbox provides functions for solving partial differential equations in 2D, 3D, and at a time using finite element analysis. It lets you specify and mesh 2D and 3D geometries and formulate boundary conditions and equations. In the case of Ordinary Differential Equations, MATLAB uses two functions, ode23, and ode45, which are capable of numerically solving differential equations. Both of them use a similar numerical formula, Range-Kutta, but to a different order of approximation.
Why learn ODE/PDE in Matrix toolbox
Partial Differential Equation Toolbox is used to solve PDEs from standard problems such as diffusion, heat transfer, structural mechanics, electrostatics, magnetostatics, and AC power electromagnetics, as well as custom, coupled systems of PDEs. If an ODE is not linear, most of the cases it cannot be solved exactly. A strong understanding of engineering mathematics, as well as basic level of programming, is required for this course.