## Procedimiento numérico

Resolver el sistema de ecuaciones diferenciales

$\begin{array}{l}\frac{{d}^{2}{V}_{1}}{d{t}^{2}}=\frac{{S}^{2}}{m}\left({k}_{1}{\left({V}_{1}\right)}^{-{\gamma }_{1}}-{k}_{2}{\left({V}_{T}-{V}_{1}\right)}^{-{\gamma }_{2}}\right)-\frac{e}{m}\frac{d{V}_{1}}{dt}\\ \frac{d{k}_{1}}{dt}=\alpha \frac{eR}{{c}_{v1}{S}^{2}}{\left(\frac{d{V}_{1}}{dt}\right)}^{2}{\left({V}_{1}\right)}^{{\gamma }_{1}-1}\\ \frac{d{k}_{2}}{dt}=\left(1-\alpha \right)\frac{eR}{{c}_{v2}{S}^{2}}{\left(\frac{d{V}_{1}}{dt}\right)}^{2}{\left({V}_{T}-{V}_{1}\right)}^{{\gamma }_{2}-1}\end{array}$

por procedimientos numéricos, con las siguientes condiciones iniciales, en el instante t=0.

$\begin{array}{l}{V}_{1}={V}_{10}\text{ }\text{ }\left(\frac{d{V}_{1}}{dt}\right)=0\\ {k}_{1}={p}_{10}{V}_{10}^{{\gamma }_{1}}\text{ }\text{ }{k}_{2}={p}_{20}{V}_{20}^{{\gamma }_{2}}\end{array}$

 `public class Estado { double t; double x; double y; double z; double v; public Estado(double t, double x, double v, double y, double z) { this.t=t; this.x=x; this.y=y; this.z=z; this.v=v; } } public class Gas { public double presion; public double volumen; public double nMoles; public double cV; public double temperatura; double gamma; public Gas(double presion, double volumen, double nMoles, boolean bMono) { this.presion=presion; this.volumen=volumen; this.nMoles=nMoles; temperatura=presion*volumen*100/(nMoles*8.3143); this.cV=(bMono)?(3*8.3143/2):(5*8.3143/2); this.gamma=(bMono)?(5.0/3):(7.0/5); } } public abstract class RungeKutta { double h; RungeKutta(double h){ this.h=h; } public void resolver(Estado e){ //variables auxiliares double k1, k2, k3, k4; double l1, l2, l3, l4; double m1, m2, m3, m4; double q1, q2, q3, q4; //condiciones iniciales double x=e.x; double v=e.v; double t=e.t; double y=e.y; double z=e.z; //for(double t=t0; t