In this work we develop an analytic approach to study pulsar spindown. We use the monopolar spindown model by , which assumes an inverse linear law of magnetic field decay of the pulsar, to extract an all-order formula for the spindown parameters which are expressed in terms of modified Bessel functions. We further extend the analytic model to incorporate the quadrupole term that accounts for the emission of gravitational radiation, and obtain expressions for the period P and frequency f in terms of transcendental equations. We derive the period of the pulsar evolution as an approximate first order solution in the small parameter present in the full solution. We find that the first three spindown parameters of the Crab, PSR B1509-58, PSR B0540-69 and Vela pulsars are within their known bounds providing a consistency check on our approach. After the four detections of gravitational waves from binary black hole coalescence and a binary neutron merger 170814, which was a novel joint gravitational and electromagnetic detection, a detection of gravitational waves from pulsars will be the next landmark in the field of multi-messenger gravitational wave astronomy.introduced to ensure that the braking indices defined in terms of the frequency and higher derivatives are in agreement with the trajectories in the P ¬Ṗ diagram for pulsar evolution, where P andṖ denote the pulsar period and its time derivative. Their detailed analysis of the stationary multipole model ruled out the possibility of a time independent evolutionary equation for the pulsar frequency. Their time dependent multipole model included dynamics of the pulsar magnetic moment and thereby the decay of the magnetic field, B(t). They show in their analysis that an inverse linear decay proposed by Chanmugham and Sang [3], in contrast to an exponential decay law for pulsar magnetic field [4], did a better fit of the evolutionary trajectories of the four pulsars studied namely the Crab, PSR B1509-58, PSR B0540-69 and Vela. Following their approach, we use an inverse linear decay law for B(t). The spindown of pulsars due to the intense magnetic fields that surround them is a phenomenon that will significantly impact on the younger pulsars which can lose a large amount of rotational energy due to physical processes such as electromagnetic and gravitational multipole radiation. The evolution of pulsars has been studied in great detail [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].The first observations of gravitational waves by Advanced LIGO are identified as black hole mergers, namely GW150914 [22], GW151226 [23] and a less significant candidate LVT151012 [24]. Recently, GWs from another such merger, GW170104 has been reported [25]. GW170814 was coherently observed by the advanced Virgo and two advanced LIGO detectors, produced by the coalescence of two stellar mass black holes. Recently, a neutron merger has been detected by both GW and electromagnetic observations [26]. With increasing detector sensitivity of LIGO, VIRGO and the upcoming KAG...