Add code for figure 2.1.

src/figure_2_1.m

+clear all
+close all
+clc
+
+k = 1;
+R1 = 10;
+R2 = 100;
+
+M = 1000;
+
+N1end = 25;
+N1_values = 0:N1end;
+N2end = 150;
+N2_values = 0:N2end;
+
+sn1 = evaluate_sn(R1,k,0:M);
+sn2 = evaluate_sn(R2,k,0:M);
+
+sum1 = zeros(1,N1end+1);
+sum2 = zeros(1,N2end+1);
+
+for iterN = N1_values
+    sum1(iterN+1) = 2*sum(sn1(iterN+1:end));
+end
+
+for iterN = N2_values
+    sum2(iterN+1) = 2*sum(sn2(iterN+1:end));
+end
+
+relsum1 = sum1 ;% / (sn1(1)+2*sum(sn1(2:end)));
+relsum2 = sum2 ;% / (sn2(1)+2*sum(sn2(2:end)));
+
+%%
+figure()
+semilogy(N1_values,relsum1,'b-','linewidth',2)
+hold on
+title('$kR=10$', 'Interpreter', 'LaTex')
+xlabel('$N$', 'Interpreter', 'LaTex')
+% ylabel('$\sum_{|n|>N}\|J_n(kR)\|^2$', 'Interpreter', 'LaTex')
+set(gca,'Fontsize',20)
+set(gca, 'Linewidth', 1.5);
+lims = axis;
+fill([lims(1) lims(1) k*R1 k*R1], [lims(3) lims(4) lims(4) lims(3)], [0.7, 0.7, 0.7], 'FaceAlpha', 0.4, 'EdgeColor', 'none');
+hold off
+grid on
+
+print decay_reminder_sum1.eps -depsc
+
+figure()
+semilogy(N2_values,relsum2,'b-','linewidth',2)
+hold on
+title('$kR=100$', 'Interpreter', 'LaTex')
+xlabel('$N$', 'Interpreter', 'LaTex')
+% ylabel('$\sum_{|n|>N}\|J_n(kR)\|^2$', 'Interpreter', 'LaTex')
+set(gca,'Fontsize',20)
+set(gca, 'Linewidth', 1.5);
+lims = axis;
+fill([lims(1) lims(1) k*R2 k*R2], [lims(3) lims(4) lims(4) lims(3)], [0.7, 0.7, 0.7], 'FaceAlpha', 0.4, 'EdgeColor', 'none');
+hold off
+grid on
+
+print decay_reminder_sum2.eps -depsc
+
+%%
+
+function y = evaluate_sn(R,k,n)
+    y = pi*(k*R)^2*((besselj(n,k*R)).^2 - besselj(n-1,k*R).*besselj(n+1,k*R));
+end
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