1 files changed, 58 insertions, 0 deletions
diff --git a/260/CH15/EX15.4/15_4.sce b/260/CH15/EX15.4/15_4.sce
new file mode 100644
index 000000000..2f31d7315
--- /dev/null
+++ b/260/CH15/EX15.4/15_4.sce
@@ -0,0 +1,58 @@
+//Eg-15.4
+//pg-617
+
+clear
+clc
+
+close()
+
+//Using equation [21] in this problem
+
+//Solving the equations analytically gives 3 equatinos in y11,y21,y31 which can be solved using matrix inversion.
+
+printf('Using the equation [21] we get :\n')
+x1 = inv([1.16 -0.08 0;-0.08 1.16 -0.08;0 -0.08 1.16])*[33;25;33];
+
+printf(' y11 = %f\n y21 = %f\n y31 = %f\n',x1(1,1),x1(2,1),x1(3,1))
+
+//Similarly solving for the elements in the column 2,3&4
+
+x2 = inv([1.16 -0.08 0;-0.08 1.16 -0.08;0 -0.08 1.16])*[43.442;26.4406;43.4442];
+
+printf(' y12 = %f\n y22 = %f\n y32 = %f\n',x2(1,1),x2(2,1),x2(3,1))
+
+x3 = inv([1.16 -0.08 0;-0.08 1.16 -0.08;0 -0.08 1.16])*[51.3531;30.0152;51.3531];
+
+printf(' y13 = %f\n y23 = %f\n y33 = %f\n',x3(1,1),x3(2,1),x3(3,1))
+
+x4 = inv([1.16 -0.08 0;-0.08 1.16 -0.08;0 -0.08 1.16])*[57.6403;34.5618;57.6403];
+
+printf(' y14 = %f\n y24 = %f\n y34 = %f\n',x4(1,1),x4(2,1),x4(3,1))
+
+y = zeros(4,5)
+
+y(1:4,1) = 100;
+y(1:4,5) = 100;
+
+y(1,2:4) = x1';
+y(2,2:4) = x2';
+y(3,2:4) = x3';
+y(4,2:4) = x4';
+
+printf('The values of y at the grid points are shown in the following table :\n')
+disp(y)
+
+printf('\nThe profiles of y by Crank-Nicolson method  is shown in the figure\n')
+
+x = 0:0.25:1;
+
+y1 = y(1,1:5);
+y2 = y(2,1:5);
+y3 = y(3,1:5);
+y4 = y(4,1:5);
+
+
+plot(x,y1,x,y2,x,y3,x,y4)
+legend('t1','t2','t3','t4')
+xlabel('x')
+ylabel('y')