Introduction to Engineering and Scientific Computing with Python

9 Solving Differential Equations

DOI: 10.1201/9781003256861-9

Chapter Objectives

• Become familiar with the different forms of differential equations encountered by engineers and scientists.
• Be able to recognize differential equations that can be solved numerically by the methods of quadrature (finding the area under the curve).
• Introduce the trapezoidal rule method for solving quadrature problems and the quad function from the SciPy integrate module.
• Understand how to solve a differential equation with the Euler method.
• Appreciate the limitations of the Euler method when it comes to the accuracy of the solution.
• See how the Heun method is an improvement in accuracy over the Euler method.
• Understand how to extend the methods to the solution ...