Efficient Jacobi–Gauss collocation method for solving initial value problems of Bratu-type

In this paper, we propose the shifted Jacobi–Gauss collocation spectral method for solving initial value problems of Bratu type, which is widely applicable in fuel ignition of the combustion theory and heat transfer. The spatial approximation is based on shifted Jacobi polynomials $J_n^{(\alpha,\beta)}(x)$ with $\alpha, \beta \in(-1,\infty)$, $x\in[0,1]$ and $n$ the polynomial degree. The shifted Jacobi–Gauss points are used as collocation nodes. Illustrative examples have been discussed to demonstrate the validity and applicability of the proposed technique. Comparing the numerical results of the proposed method with some well-known results show that the method is efficient and gives excellent numerical results.