diff --git a/src/PDSProblemLibrary.jl b/src/PDSProblemLibrary.jl index fe654741..998f5b64 100644 --- a/src/PDSProblemLibrary.jl +++ b/src/PDSProblemLibrary.jl @@ -92,7 +92,7 @@ u_2' &= 0.04u_1-10^4 u_2u_3-3⋅10^7 u_2^2,\\\\ u_3' &= 3⋅10^7 u_2^2, \\end{aligned} ``` -with initial value ``\\mathbf{u}_0 = (1.0, 0.0, 0.0)^T`` and time domain ``(0.0, 10^11)``. +with initial value ``\\mathbf{u}_0 = (1.0, 0.0, 0.0)^T`` and time domain ``(0.0, 10^{11})``. There is one independent linear invariant, e.g. ``u_1+u_2+u_3 = 1.0``. ## References diff --git a/src/mprk.jl b/src/mprk.jl index 5b8e8878..65594914 100644 --- a/src/mprk.jl +++ b/src/mprk.jl @@ -751,7 +751,7 @@ non-negative Runge--Kutta coefficients. Each member of this family is a one-step method with four-stages which is third-order accurate, unconditionally positivity-preserving, conservative and linearly implicit. In this implementation the stage-values are conservative as well. The parameter `γ` must satisfy -`\\frac{3}{8}≤ γ≤\\frac{3}{4}`. +`3/8 ≤ γ ≤ 3/4`. Further details are given in Kopecz and Meister (2018). These modified Patankar-Runge-Kutta methods require the special structure of a