Computational Physics

Computational physics is a sub-discipline that employs numerical analysis and computer simulations to solve complex physical problems that are often intractable with purely analytical methods. Functioning as a crucial bridge between theoretical and experimental physics, it allows scientists to model and investigate phenomena ranging from the quantum behavior of materials to the large-scale evolution of the cosmos. By developing algorithms and leveraging computational power, this field not only tests theoretical predictions but also guides the design of new experiments, effectively serving as a third pillar of modern scientific inquiry in physics.

1. Introduction to Computational Physics
   1. Definition and Scope
   2. Historical Development
      1. Early Computing in Physics
      2. Evolution of Numerical Methods
      3. Modern Computational Physics Era
   3. Role of Computation in Physics
      1. Theory-Experiment Bridge
      2. Numerical Experiments
      3. Predictive Modeling
      4. Visualization of Physical Phenomena
   4. Types of Computational Problems
      1. Analytical vs Numerical Solutions
      2. Deterministic vs Stochastic Methods
      3. Continuous vs Discrete Models
   5. Limitations and Challenges
      1. Computational Complexity
      2. Accuracy vs Efficiency Trade-offs
      3. Verification and Validation