Computational Methods

• Computational methods refer to the techniques that use computers to solve problems involving calculations.
• They are used in a wide range of disciplines, such as physics, engineering, applied mathematics, statistics, and computer science.
• The basic process involves designing algorithms to perform specific computations and then implementing them using a programming language.
• A problem must first be defined clearly and understandingly; this includes the expected inputs and outputs, as well as the steps needed to turn the former into the latter.
• The chosen solution should be verified against a range of test cases to ensure it produces the correct results consistently. An important aspect is comparison testing.
• Pseudocode and flowcharts are common tools used in the design and visualisation of the algorithm before its implementation.
• Algorithms can be categorised into different types, including recursive, search and sort, divide and conquer, greedy, and dynamic programming, each with its advantages and disadvantages.
• Complexity analysis is fundamental in computational methods. It involves assessing both the time and space needs of an algorithm and how these change as the input size increases.
• Computational methods also involve error analysis, identifying and examining the sources of error in computational results.
• Debugging is an essential skill for resolving errors in code. It involves identifying the section of code causing the problem, understanding why it’s causing an issue, and then resolving it.
• Version control systems, such as Git, are useful tools for keeping track of changes to code and allowing for collaborative work.
• Implementing computational methods requires a strong understanding of a programming language, whether it be Python, JavaScript, Java, or another language.
• Modelling and Simulation are crucial principles under computational methods and techniques. They create a representation of a real system and imitate its behaviour.
• Code should be commented and written in a clear and concise manner to aid future maintenance and understanding.
• Basic operations of computational methods include arithmetic operations, control structures, groupings and assignments, and data structure manipulation.
• Privacy, security, and ethical considerations are vital in computational methods. Considerations should be given to the handling and storage of data, its accessibility, and the potential implications of a security breach.