In numerical analysis, there are several properties that we need to consider when solving mathematical problems using MATLAB. Here are three properties of numerical analysis in MATLAB:
Accuracy: Accuracy refers to the degree of closeness of the calculated value to the actual value of the solution. In MATLAB, we can increase the accuracy of the numerical solution by adjusting the tolerance level of the solver. For example, if we use the ode45 function to solve a differential equation, we can set the relative and absolute tolerances using the 'RelTol' and 'AbsTol' options to get a more accurate solution.
Stability: Stability refers to the property of numerical methods that ensures that the solutions do not become highly sensitive to small changes in the initial conditions or the parameters of the problem. In MATLAB, we can ensure stability by using appropriate numerical methods and applying stability conditions. For example, if we are solving a heat equation using the finite difference method, we need to ensure that the time step is small enough to ensure stability.
Convergence: Convergence refers to the property of numerical methods that ensures that the solution approaches the true solution as we refine the mesh or increase the order of the numerical method. In MATLAB, we can check the convergence of the numerical method by comparing the solution obtained at different mesh sizes or orders of the method. If the solution is converging to a steady-state solution, then the numerical method is said to be convergent.
gistlibby LogSnag