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nbann5000
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can anyone direct me to a website that gives adequate treatment of the numerical solution of partial differential equations, especially pertaining to problems which involve the use of the Crank-Nicolsen procedure?
Applied Numerical Methods, Luther, Carnahan, and Wilkesnbann5000 said:can anyone direct me to a website that gives adequate treatment of the numerical solution of partial differential equations, especially pertaining to problems which involve the use of the Crank-Nicolsen procedure?
An analytical solution is a closed-form solution that can be expressed using mathematical equations and can be solved exactly. On the other hand, a numerical solution uses numerical methods to approximate the solution to a partial differential equation. This is necessary for complex equations where an analytical solution is not possible.
Some commonly used numerical methods for solving partial differential equations include finite difference methods, finite element methods, and spectral methods. Each method has its own advantages and is suitable for different types of equations and boundary conditions.
The accuracy of a numerical solution for a partial differential equation can be determined by comparing it to the exact analytical solution, if available. Otherwise, the solution can be compared to results obtained using a finer grid or by varying the step size in the numerical method. A lower error indicates a more accurate solution.
Yes, numerical solutions of partial differential equations are commonly used for real-world applications in many fields such as engineering, physics, and finance. They provide a practical and efficient way to solve complex equations and can be used to model and predict real-world phenomena.
Yes, there are some limitations to numerical solutions of partial differential equations. The accuracy of the solution depends on the chosen numerical method and grid size, and it may not always be possible to obtain an accurate solution in a reasonable amount of time. Additionally, the solution may also be affected by numerical errors and round-off errors.