@Preben Alsholm Thanks for the suggestion. However, do I need to find the difference between the values of h and h/2 in order to deduce the convergence value? But in one literature, I saw this statement ''convergence is achieved only when the absolute value of every unknown approximations differ by 10^-5 at all values of x in 0<x<infinity''

Best regards.

@Preben Alsholm  How can one check for the convergence from the solution obtained in maple.

Best regard.

@sazroberson  theta[3] has been removed from the fsolve and the error is now
'' Error, (in fsolve) number of equations, 1, does not match number of variables, 9 ''

The aim of solving this coupled BVP is to use the values from soln1 in ode2 so that ode2 will be solved compltely. see the worksheet p4.mw

@Preben Alsholm I really appreciate your effort. In eq[12] you have used the central difference instead of backward difference and that's the reason for defining bd. However, I'm working on the guess value so that the result from the finite difference is all most that of the closed-form.

Best regards.

@Preben Alsholm  Good day and thanks for suggestion. The purpose of linearizing is to be able solve the coupled non-linear BVP with finite difference method. Here is the actual problem Linearize_1.mw 

Somebody suggested linearizing ode1 before applying the finite difference scheme. Please help!!!

Best regards.

@Kitonum Good day, are you suggesting that I should define eq[j] for ode2? Because I got the same error even when solving for ode1 only. Please help.

Thank you.

@Preben Alsholm  The values of k_1 are in L.

@Preben Alsholm  Thanks so much, it works. I'm very grateful.

@Prebe Alsholm the idea you gave me still return error. however, i need to write maple programme to solve the new one i just posted using any good method. thanks for your interest.

@Carl Love 

4th_order.mw

4th_order.mw please take a look at it.

Thanks. 

@Carl Love 

Good day,thanks so much for the hint, it works.

Thanks.

@Carl Love 

My goal is to solve the ode numerically using RK4 in maple.

Thanks.