Questions on numerical analysis/numerical methods; methods for approximately solving various problems that often do not admit exact solutions.

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Runge Kutta 8(5,3)

This is actually three small very related questions about Runge Kutta methods. 1) I have programmed a RK 7(8) method also RK 4(5). At the beginning I was assuming that the RK 7(8) uses two ...
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numerical method (implicit , backward difference or forward difference) for nonlinear pde

$\newcommand{\lbar}{\underline{\lambda}}$ In this linear PDE: \begin{cases} B_t+b^Q(r,t)B_r+\frac{1}{2}d^2(r,t)B_{rr}+(\mu(\lambda,t)+\alpha \sigma (t))(\lambda -\lbar)B_{\lambda} \\ ...