MATLAB: Issue with solving an expression using solve command

cognitive radiosolve

I am doing coding for my thesis in Cognitive Radio Systems. After a series of simplification and substitution I got following expression for R_new which is the function of t_new
R_new=29310*t_new - (740230637807590039*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1))/9007199254740992 + (553376302050334301*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(31*t_new^(1/2) - 2383690921325797/562949953421312))/2) - 1))/9007199254740992 + (2982482666894658895*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(26*t_new^(1/2) - 7691227197842525/2251799813685248))/2) - 1))/18014398509481984 + (6130259553882274789*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(32*t_new^(1/2) - 618966936424713/140737488355328))/2) - 1))/36028797018963968 + (2335679196965696725*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(25*t_new^(1/2) - 3661259950175195/1125899906842624))/2) - 1))/18014398509481984 + (495882660278870997*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(81*t_new^(1/2) - 1748195917190933/140737488355328))/2) - 1))/18014398509481984 + (380895376735944389*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(74*t_new^(1/2) - 6347298562227079/562949953421312))/2) - 1))/9007199254740992 + (4391076890295509843*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(35*t_new^(1/2) - 688099554704501/140737488355328))/2) - 1))/36028797018963968 + (2810001741580268983*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(37*t_new^(1/2) - 2936751867564147/562949953421312))/2) - 1))/36028797018963968 + (4247342785866851583*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(38*t_new^(1/2) - 6057857383874553/1125899906842624))/2) - 1))/18014398509481984 + (725857227364724213*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(27*t_new^(1/2) - 4029967247667347/1125899906842624))/2) - 1))/4503599627370496 + (4031741629223864193*2^(1/2)*pi^(1/2)*(erf((2^(1/2)*(39*t_new^(1/2) - 6242211032620389/1125899906842624))/2) - 1)*((10*t_new)/3 - 1))/36028797018963968 + (1660128906151002903*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(23*t_new^(1/2) - 3292552652683065/1125899906842624))/2) - 1))/9007199254740992 + (1573888443493807947*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(51*t_new^(1/2) - 8454454817717421/1125899906842624))/2) - 1))/36028797018963968 + (1617008674822405425*2^(1/2)*pi^(1/2)*((10*t_new)/3 - 1)*(erf((2^(1/2)*(24*t_new^(1/2) - 1738453150714565/562949953421312))/2) - 1))/9007199254740992
now I need to calculate the value of t_new, which can be solved by taking the derivative and setting it to zero for this I did
R_derivative= diff(R_new)
t=solve(R_derivative)
but I am getting following result
Warning: Explicit solution could not be found. In solve at 83 In algorithm_temp at 84
t =
[ empty sym ]
but when I solve R_new for t_new it will give exact value. why I can't solve R_derivative ?
thanks in advance !!

Best Answer

Are you getting a symbolic solution for t_new from the R_new expression? One that is not expressed in terms of RootOf() ? I do not seem to be able to eliminate the RootOf(). If you are substituting in a numeric value for R_new then the solver would do a numeric solution rather than an exact solution.
The numeric solution for the differential is approximately 0.04082971273
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