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Jul
12
revised Solve the following differential equations by converting to Clairaut's form through suitable substitutions.
added 1768 characters in body
Jul
11
answered Black Scholes Merton PDE with a time variant boundary condition
Jul
11
comment Black Scholes Merton PDE with a time variant boundary condition
A few questions: Is there a relationship between $r$, $\delta$ and $\sigma$? Are all constants positive? One bigger than the other, etc? What's the domain for $V$? What's the behavior you're expecting for $S$ as the price $V$ goes to infinity?
Jul
9
revised Is this function bounded? Next question about integral $\int_{\partial M} \frac{1}{||y-x||} n_y \cdot \nabla_y \frac1{||y-x||} dS_y$.
added 70 characters in body
Jul
9
comment Solution of a differentiation in integral form
@ComplexGuy Nope, the definition of Spherical Bessel functions is \begin{align}j_n(x) &= \sqrt{\frac{\pi}{2 x}} J_{n + \frac{1}{2}}(x) \\ \\ y_n(x) &= \sqrt{\frac{\pi}{2 x}} Y_{n + \frac{1}{2}}(x)\end{align}
Jul
8
answered Is this function bounded? Next question about integral $\int_{\partial M} \frac{1}{||y-x||} n_y \cdot \nabla_y \frac1{||y-x||} dS_y$.
Jul
8
comment How to find out where a solution to a differential equation is defined?
The answer to your question is that theorem. Any ODE book will have a detailed proof, along with the relation between existence, uniqueness and continuation of solutions depending on parameters and initial conditions.
Jul
8
comment Ordinary Differential Equations - Sturm Liouville
Hint: Sturm separation theorem
Jul
8
revised How to find out where a solution to a differential equation is defined?
edited tags
Jul
8
comment How to find out where a solution to a differential equation is defined?
Have you read the Picard–Lindelöf theorem?
Jul
8
comment Solve the following differential equations by converting to Clairaut's form through suitable substitutions.
@Vish.Math See the edit. If you find it appropriate, please consider accepting the answer.
Jul
8
revised Solve the following differential equations by converting to Clairaut's form through suitable substitutions.
Improved the answer to address OP's concerne.
Jul
8
revised Solution of a differentiation in integral form
edited tags
Jul
8
revised Solution of a differentiation in integral form
deleted 1 characters in body
Jul
8
comment Solution of a differentiation in integral form
No offence, but it is my impression that you might be reading something more complex than you can handle right now. You really need to step up your knowledge on special functions, separation of variables, eigenfunctions and eigenvalues, Fourier and Laplace transforms, etc. if you want to fully understand the maths that are being used in the articles you are trying to read.
Jul
8
answered Solution of a differentiation in integral form
Jul
5
comment Plotting graphs using numerical/mathematica method
@ComplexGuy In your first plot, you have the wrong code. In the second term inside the root it says 3*2^(1 + 2)*A while it should say 32^(1 + 2)*A.
Jul
5
comment Complex integral - winding number
@MhenniBenghorbal Pretty sure. Robjohn's answer address this.
Jul
5
comment Evaluating decay rate with trigonometric explanation
@ComplexGuy Show[Plot[Evaluate[{A/(1 + 2 t^2/R^4)^(3/4) Cos[Sqrt[2] t + 3/2 ArcTan[(Sqrt[2] t)/R^2]], A/(1 + 2 t^2/R^4)^(3/4), -(A/(1 + 2 t^2/R^4)^(3/4)), A/E} /. {A -> 2, R -> 3}], {t, 0, 12}, PlotStyle -> {Red, {Black, Dashed}, {Black, Dashed}, Blue}, AxesLabel -> {"t", "\[Phi](0,t)"}, ImageSize -> 400], Graphics[{Black, PointSize[0.02], Point[{((E^(4/3) - 1)/2)^(1/2) R^2, A/E}], {Black, Line[{{((E^(4/3) - 1)/2)^(1/2) R^2, 0}, {((E^(4/3) - 1)/2)^(1/2) R^2, A/E}}]}}] /. {A -> 2, R -> 3}]
Jul
5
comment Evaluating decay rate with trigonometric explanation
@ComplexGuy See the edit.