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Q: Why euler method is not applicable for Partial Differential Equations?
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What is the theory of finite differential method?

Finite Differential Methods (FDM) are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.


Which numerical method for solving differential equations methods gives the most inaccurate result?

Euler's Method (see related link) can diverge from the real solution if the step size is chosen badly, or for certain types of differential equations.


How do you solve hamilton jacobi equations of motion?

This method was governed by a variational principle applied to a certain function. The resulting variational relation was then treated by introducing some unknown multipliers in connection with constraint relations. After the elimination of these multipliers the generalized momenta were found to be certain functions of the partial derivatives of the Hamilton Jacobi function with respect to the generalized coordinates and the time. Then the partial differential equation of the classical Hamilton-Jacobi method was modified by inserting these functions for the generalized momenta in the Hamiltonian of the system.


Who invented the method of undetermined coefficients?

Leonhard Euler developed this method in his article, "De aequationibus differentialibus, quae certis tantum casibus integrationem admittunt (On differential equations which sometimes can be integrated)," published in 1747.


How does the method for solving equations with fractional or decimal coefficients and constants compare with the method for solving equations with integer coefficients and constants?

The method is the same.