Question

Q4. Obtain a fourth order of accuracy approximation formula for " (0). You can make use of MATLAB software to find the unknown coefficients.

Q4. Obtain a fourth order of accuracy approximation formula for y'' (0). You can make use of MATLAB software to find the unknown coefficients

Answer 1

y(0)=0,

y(π/2)−2=0.

The corresponding function is

function res = bcfcn(ya,yb)
res = [ya(1)
       yb(1)-2];
end

Create Initial Guess

Use the bvpinit function to create an initial guess for the solution of the equation. Since the equation relates y′′ to y, a reasonable guess is that the solution involves trigonometric functions. Use a mesh of five points in the interval of integration. The first and last values in the mesh are where the solver applies the boundary conditions.

The function for the initial guess accepts x as an input and returns a guess for the value of y1 and y2. The function is

function g = guess(x)
g = [sin(x)
     cos(x)];
end

xmesh = linspace(0,pi/2,5);
solinit = bvpinit(xmesh, @guess);