If you're doing this on your back you're going to hate life but it has to be done. disconnect the battery FIRST! put vehicle on jack stands at frame behind front wheels. pull the front tires. drain oil from front diff. remove both brake calipers from spindle assy.[dont remove the brake lines] then swing out of the way and secure so they dont hang. unplug the a.b.s wire and remove from all harness clips. remove nut from outer tie rod end and whack SPINDLE to loosen end then swing out of the way. loosen the lower ball joint nut till its only on by a couple of threads. remove the pinch nut and bolt from the upper ball joint [pull or tap down on control arm, bolt should slide out.] whack SPINDLE!! on lower a few good times to loosen ball joint[ hit the spindle only plz.] remove the nut and take spindle and brake assy off and set it aside. do same for both sides. drain oil from pan. remove plug then find the 4 bolts that hold actuator to oil pan. [right side] then remove the actuator.[if the shaft comes with it pull it out from actuator, remove actuator first then slide shaft out. pull the serpentine belt off the a/c compressor but leveraging the tensioner to loosen belt. remove the 4 bolts holding compressor to oil pan and swing compressor out of the way. remove the 4 bolts from the skid plate under oil pan then remove all the bolts from large frame looking skid plate [4 big ones are 22mm] then for the brace behind that plate [should only have 2 left after removing the plate] take the 4 bolts out holding the front drive shaft to the diff. [7/16] pry the u joint out. then remove the 4 bolts holding the front diff to the pan, wiggle the front diff out of the pan and secure it away from the pan with a bungee cord or something. now! pay attention!! put the steering wheel in the straight ahead position remove the key so it locks. remove the 10mm bolt where the lines go into the rack and pull the lines off[watch for o rings] catch fluid in a pan. lift up on the soft boot at steering shaft youll see a 13mm bolt take it out and remember which way it was facing!! pull the 2 big horizontal bolts and nuts and remove the rack. keep dirt out of the holes for lines. now remove the [ 3] 10mm bolts at front of the oil pan. pull the rubber plugs out at bottom of bell housing and remove the  10mm bolts from back of oil pan. remove all bolts from oil pan [13mm] except leave 1 on either side loosely in use LIGHT STEADY pressure to unstick pan from silicone. once its loose pull the 2 last bolts and drop the pan. [if it wont loosen up MAKE SURE YOU GOT ALL THE BOLTS OUT. especially in the right front corner, theres one that kinda hides up there.] then you can drop the front diff out. reverse procedure to install. clean all the old silicone off the pan. use grey silicone or "the right stuff" [come on people..quit using the blue silicone....] or else you may be doing it again. remember you only need a thin bead [thick as a nickle, i smooth it down with my finger, make sure you cover entire surface] dont glob it on , its not necessary. use 75w-140 synth. gear oil for diff. make sure bearings are clean and greased in actuator. make sure you slide the shaft back in on rack [remember which way the bolt was facing? is it still there? dont turn the freaking wheel with rack out or air bag may explode in your face when you reconnect battery! dont forget to put oil back in the engine or you just ruined your day. took me around 4-5 hours on a lift figure 8-9 on back. but you just saved yourself around $600.
If you are talking about slack in the gears in the differential , then you will have to replace them because they have alot of wear and don't fit together snug any more . If you are talking about the whole differential having play and making a clunking noise when you pull away from a stop , then you need to change the rubber bushings at each end of your leaf springs .
The Runge-Kutta method is one of several numerical methods of solving differential equations. Some systems motion or process may be governed by differential equations which are difficult to impossible to solve with emperical methods. This is where numerical methods allow us to predict the motion, without having to solve the actual equation.
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