InWilson and Newmark method the temporal difference equations are combined with the current equations of motion and the resulting equations are solved to find the current displacement. They belongs to the category of implicit integration method.

WILSON METHOD

• • The Wilson method is also known as Wilson θ method. If θ =1.0, this method reduces to the linear acceleration scheme. It can be described by the following steps:
• From the known initial conditions and , find using equation
  
  
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Select a suitable time step Δt and a suitable value of θ ( θ is usually taken as 1.4).

• • In Wilson method it is assumed that the acceleration of the system varies linearly between two instant of time
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  • Compute the effective load vector starting with i= 0:
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Find the displacement vector at time

• • Calculate the acceleration, velocity and displacement vectors at time :
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