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It happens when the solution for the equation is periodic and contains oscillatory functions such as cos, sin and their combinations.

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Why you need the numerical solution of partial differential equations?

Very often because no analytical solution is available.


What is a numerical solution of a partial differential equation?

Some partial differential equations do not have analytical solutions. These can only be solved numerically.


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.


What are the Sample problems in differential equations?

Sample problems in differential equations often include finding the solution to first-order equations, such as separable equations or linear equations. For example, solving the equation ( \frac{dy}{dx} = y - x ) involves using integrating factors or separation of variables. Other common problems include second-order linear differential equations, like ( y'' + 3y' + 2y = 0 ), where the characteristic equation helps find the general solution. Applications may involve modeling real-world phenomena, such as population growth or the motion of a pendulum.


What is WKB methodHow you get solutions of differential equations using WKB method?

The WKB (Wentzel-Kramers-Brillouin) method is a semiclassical approximation used to find solutions to linear differential equations, particularly in quantum mechanics and wave phenomena. It involves assuming a solution in the form of an exponential function, where the exponent is a rapidly varying phase. By substituting this form into the differential equation and applying asymptotic analysis, one can derive an approximate solution valid in regions where the potential changes slowly. This method is particularly useful for solving Schrödinger equations and other second-order linear differential equations in physics.

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Why you need the numerical solution of partial differential equations?

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