Meshless methods are gaining popularity for numerically solving the governing equations of Fluid Dynamics primarily because they do not require the generation of grid around the given geometry in the computational domain. They just require a point distribution with a proper connectivity, which is extremely simple to generate as compared to the grid around complex geometries. However, obtaining a higher order accurate numerical solution is difficult in case of meshless methods as it requires either a solution of a larger system of linear algebraic equations, or defect correction method coupled with inner iterations. This method becomes too much complicated if still further higher order accuracy is desired. Here an alternate method based on Modified Partial Differential Equations has been used to obtain higher order accurate solution using the meshless methods. The basic idea behind the new approach is to explicitly remove the truncation error from the Modified Partial Differential Equation (formed from the governing equations) and numerically solve the resulting equation with the meshless technique. This technique has been successfully applied for the simulation of subsonic, weak transonic, strong transonic and supersonic flow past NACA0012 aerofoil. A good match of the numerical results with the standard test results of AGARD/GAMM workshop has been.