In this work, linear and nonlinear collisionless electrostatic simulation studies of the standard and short wavelength ion temperature gradient mode (SWITG) for experimental profiles and parameters of ADITYA-U tokamak are performed using the linear global eigenvalue gyrokinetic code GLOGYSTO and the nonlinear global gyrokinetic particle-in-cell code ORB5. All simulations are carried out with non-adiabatic ions and adiabatic electrons. The ADITYA-U tokamak which has recently been upgraded to divertor configuration, is small in size and well suited for investigation of micro-instabilities in the presence of density and temperature gradients. Due to steep density and temperature gradients, simulation shows that the SWITG mode naturally exists along with the standard ion temperature gradient (ITG) mode in ADITYA-U. In this work, the experimental shot# 33536 of the ADITYA-U tokamak is considered as a reference. There is good agreement in the growth rate and the real frequency values between GLOGYSTO and ORB5 with variations of less than 25%. Two maxima of growth rate versus mode number are obtained, the first around k(theta)rho(s) similar or equal to 0.4 is the standard ITG, the second around k(theta)rho(s) similar or equal to 1.2 is the SWITG. Additionally, using linear stability analysis, it is observed that the SWITGs are suppressed for low values of R-0/L-T i.e. only the standard ITG mode remains unstable. For the ADITYA-U tokamak, nonlinear global simulations with ORB5 are also carried out. Nonlinearly, SWITG dominating case results are compared with the conventional ITG case, where SWITG is relatively suppressed. The nonlinear contribution of the SWITG mode to the total thermal ion heat transport is found to be minimal due to an increased zonal flow shearing effect on the SWITG mode suppression, even though it may be linearly more unstable than the conventional long wavelength (k(theta)rho(s) similar or equal to < 1) ITG mode.