The B-spline collocation methods and a new ODEs solver based on B-spline quasi-interpolation are developed to study the problem of forced convection over a horizontal flat plate, numerically. The problem is a system of nonlinear ordinary differential equations which arises in boundary layer flow. A more accurate value of $$\sigma =f^{\prime \prime }(0)$$ σ = f ″ ( 0 ) obtained by applying quartic B-spline collocation method and utilized to solve the system of ODE. The results are shown to be precise as compared to the corresponding results obtained by Howarth.