% comparacion de las energias de superficie

% solucion exacta, cantidad de terminos
figure(1); clf; hold on
plot([0:0.01:1],    (sin(pi        *(1-[0:0.01:1])).^2./(pi         ).^3),'k-')
plot([0:0.01:1], sum(sin(pi*[1:2]'.*(1-[0:0.01:1])).^2./(pi * [1:2]').^3),'g-')
plot([0:0.01:1], sum(sin(pi*[1:5]'.*(1-[0:0.01:1])).^2./(pi * [1:5]').^3),'r-')
plot([0:0.01:1], sum(sin(pi*[1:10]'.*(1-[0:0.01:1])).^2./(pi * [1:10]').^3),'b-')
plot([0:0.01:1], sum(sin(pi*[1:20]'.*(1-[0:0.01:1])).^2./(pi * [1:20]').^3),'m-')
plot([0:0.01:1], sum(sin(pi*[1:50]'.*(1-[0:0.01:1])).^2./(pi * [1:50]').^3),'y-')
xlabel('r')
ylabel('1/(A D) * Es [u_0 H^2/2]')

% solucion exacta y solucion aproximada
figure(2); clf; hold on
plot([0:0.01:1], 0.5*[0:0.01:1].^2 .* (1-[0:0.01:1]).^2,'k--','linewidth',1.5)
plot([0:0.01:1],    (sin(pi*[1:1]'.*(1-[0:0.01:1])).^2./(pi * [1:1]').^3),'k-')
plot([0:0.01:1], sum(sin(pi*[1:100]'.*(1-[0:0.01:1])).^2./(pi * [1:100]').^3),'k-','linewidth',1.5)
xlabel('r')
ylabel('1/(A D) * Es [u_0 H^2/2]')

% solucion exacta y solucion aproximada, derivadas
figure(3); clf; hold on
plot([0.005:0.01:0.995],100* diff(sum(sin(pi*[1:100]'.*(1-[0:0.01:1])).^2./(pi * [1:100]').^3)),'k-','linewidth',1.5)
plot([0.005:0.01:0.995],100* diff((sin(pi*[1:1]'.*(1-[0:0.01:1])).^2./(pi * [1:1]').^3)),'k-')
plot([0.005:0.01:0.995],100* diff([0:0.01:1].^2 .* (1-[0:0.01:1]).^2)/2,'k--','linewidth',1.5)
xlabel('r')
ylabel('1/(A D) * dEs/dr  [u_0 H^2/2]')