1320.sagews

# Mathematical Methods /Numerical codes
#http://www.uprh.edu/rbaretti
#http://www.uprh.edu/rbaretti/methodsoftheoreticalphysics.htm
#http://www1.uprh.edu/rbaretti/MethodsofTheoreticalPhysicsPart2.htm
#http://www1.uprh.edu/rbaretti/MethodsofTheoreticalPhysicsPart3.htm
#http://www1.uprh.edu/rbaretti/MethodsofTheoreticalPhysicsPart4.htm
#http://www1.uprh.edu/rbaretti/MethodsofTheoreticalPhysicsPart5.htm



2.  Numerical Solution of Volterra Integral Equation of the Second Kind

3.Numerical Solution of Volterra Integral Equation of the First Kind 

4.Numerical Solution of Fredholm Equation of the second Kind 

5. Eigenvalues of Integral Equations 

6. Eigenvalues of Integral Equations -Part 2 

# www.geocities.com/serienumerica4


f=x*(1-(x+1)*exp(-x))
 
diff(f,x)

-(x + 1)*e^(-x) + ((x + 1)*e^(-x) - e^(-x))*x + 1

c2,c3=var('c2,c3')
c1=1;lambda= 9.8696544; k11=0.10119; k12= 0.60232e-09; k13=-0.34367e-02; k21=k12; k22= 0.25002e-01;k23=-0.34627e-08 ; b1=-(k11-lambda) ;b2=-k21;
solve([k12*c2+k13*c3==b1,(k22-lambda)*c2+ k23*c3==b2],c2,c3)

Syntax Error: solve([k12*c2+k13*c3==b1,(k22-lambda)*c2+ k23*c3==b2],c2,c3)

c2,c3=var('c2,c3')
a11=1 ;a12=3;a21=a12;a22=5;b1=3; b2=8;
solve([a11*c2+a12*c3==b1,a21*c2+ a22*c3==b2],c2,c3)

[[c2 == (9/4), c3 == (1/4)]]

c2,c3=var('c2,c3')
#c1=1;lambda= 9.8696544;mu=1/lambda; k11=0.10119; k12= 0.60232e-09; k13=-0.34367e-02; #k21=k12; k22= 0.25002e-01;k23=-0.34627e-08 ; b1=-(k11-mu) ;b2=-k21;
lambda= 9.869;mu=1/lambda;
k12=1;k13=3;b1=4;k22=5;k23=-2;b2=5;
solve([k12*c2+k13*c3==b1,(k22-mu)*c2+ k23*c3==b2],c2,c3)

Syntax Error: k12=1;k13=3;b1=4;k22=5;k23=-2;b2=5;

#φ1(x)normalized = ( 1.0014441 )-1/2 * {Ψ1 (x) + -0.0380019285Ψ3 (x) } 
psi1(x)=(30)^(1/2)*x*(1-x);
psi2(x)= 2*(210)^(1/2)*( x^2*(1-x)  -(1-x)*x/2 );
psi3(x)=(17640)^(1/2)*(x^3*(1-x) - ((30)^(1/2)/105 )*psi1(x) -( 1/(2*(210)^(1/2)))*psi2(x)); 
g1n(x)=( 1.0014441 )^(-1/2)*(psi1(x)  -0.0380019285*psi3(x));
y=plot(sqrt(2)*sin(pi*x),x,0,1);
show(y)