Re: How to remove a singularity

*To*: mathgroup at smc.vnet.net*Subject*: [mg130536] Re: How to remove a singularity*From*: "Ralph and Dominique Crenshaw" <raldom at verizon.net>*Date*: Fri, 19 Apr 2013 01:18:07 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20130418093435.829D36A66@smc.vnet.net>

William, maybe one of the approaches below would be useful. The first approach uses DownValues to define a singularity and the second uses a condition to cover a range of values. I would appreciate knowing if either of these approaches works for your case. Best regards, Ralph sync[x_]:=Sin[x]/x sync[0]:=1 {sync[0],sync[0.1]} {1,0.998334} sync1[x_]:=Sin[x]/x sync1[x_]:=1/;x<0.01 {sync1[.1],sync[.001]} {0.998334,1.} -----Original Message----- From: William Duhe [mailto:williamduhe at hotmail.com] Sent: Thursday, April 18, 2013 5:35 AM To: mathgroup at smc.vnet.net Subject: [mg130536] How to remove a singularity Bellow I have a differential equation which hits a singularity at low values of t. What I want to do is somehow utilize the WhenEvent command in order to replace the last factor of the equation (2/t a'[t]) with 0 at low values of t in order to avoid getting errors. Is there a way to do this? Here is an example of the equation and how I attempted to use the Whenevent Command. q = NDSolve[{a''[t] == 1/2 a[t]^2 + 1/6 a[t]^6 - 1/4 a[t]^4 - 2/t a'[t], a[0] == 1, a'[0] == 0, WhenEvent[t < .1, a'[t] -> 0]}, a, {t, 0, 1}]; any help would be appreciated!

**References**:**How to remove a singularity***From:*William Duhe <williamduhe@hotmail.com>