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These are replies submitted by AHSAN

@acer streamline means countour plots for the given ODE for the given values parameters. for refernce please have look on the figure. Beside this sir, is it possible to plot  the tabuler values for Analytic and Numeric solution against y togetherly  in a single graph and Abs.error versus  y as a separate graph?


@acer Thanks a lot, sir for your help. My series solution has a lot of other parameters due to some assumptions, which may be doubtful. To check the error or accuracy of my series solution, I solved it numerically. Sir, I have the two following: 

1: How do I check the convergence or validity of the numeric method?

2: Is it possible to draw a streamline pattern or countour plot directly from the given system of ODEs because I always draw by considering stream functions, and it takes a lot of computation and steps.

@acer I obtained series solutions (analytic solutions) for my ODE, and for simplicity, I do not give the details here. I want to compare my analytic solution with the numeric method to check the accuracy or error, which means the absolute error of the analytic solution and the numeric solution. The error is zero zero, how to find absolute error. Is it possible to write or check the convergence of the numeric method, or how could we check the convergence of the method for this problem?

@acer thanks sir. By the way, when I run same file in Maple 22, the view is not similar to what you uploaded. Is this a setting problem?

@acer Thanks, sir. phi is the main function for which I plotted the contour and then converted into 2D by p1...........Is it possible view 3D as like in the picture uploaded below?

@mmcdara you right my mistake about use of code. I have run simple code on same expression but the answer is different. Please have look on attached file. Beside this, is it possible to fixed all parameters and chnage only one means ( fix= N, beta, m] and change Br=, for every value of Br the value of x0 is different which is given in the file you uploaded. 



@mmcdara sir, I have changed the expression and followed the same procedure that you defined in the above file, but there is an error in my attempt. And is it possible to check errors for all obtained answers in tabulated form rather than apply them one by one?



@mmcdara thanks for help. Let me try for some other expressions. 

@mmcdara Sometimes it is not possible to write an expression in terms of either lambda or x. That is why I am interested in learning how to make data points directly.....and how to use the curve-fitting polynomial command.

@acer sir waiting for your response.

@acer you are right; I posted this question in December, and even you response to my question. Later, when I replied to your response, my reply was automatically deleted, and even several times I followed up on my qurey to to my question, but my reply was automatically deleted after some time. That is why I edited my question yesterday. 

My system does not have eta and I want to draw a stream line between y and x. Sir I have deleted x=0 in the file you uploaded above, and after that, my file is not producing results. Besides that, the expected result picture was uploaded to the question. Can you please help with this regard?

A few days ago, @acer helped me regarding my problem, but the replay has been deleted.

My system contains x and y; do not depend on eta. Regrading x=0, if I do not assign it to zero, do not get the results. Otherwise, there is no need to put x=0 because I am interested in plotting streamplots between y and x (y on the vertical axis and x on the horizontal axis). Besides this, I solved this system analytically, then considered the stream function, did some steps, and plotted the stream line. It is different from the stream function, which has been obtained directly by using the numeric method. I have assigned the values to parameters that I used during the analytical plot. I put x=0, and did not get the answer. Besides,  I am uploading the graph as a reference, which I have obtained by considering the stream function. This plot is similar to my flow direction, and I expect the same results from the numeric method..


@Hullzie16 I have added the ODEs


@acer Is it possible to check the residual error at once for the above file that you corrected... There are nine results and I am checking one by one by putting

evalf(eval(F, x = 0.009501474277))

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