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The purpose of this paper is to simulate numerical solutions of nonlinear Burgers' equation with two well‐known problems in order to verify the accuracy of the cubic B‐spline differential quadrature methods.

Cubic B‐spline differential quadrature methods have been used to discretize the Burgers' equation in space and the resultant ordinary equation system is integrated via Runge‐Kutta method of order four in time. Numerical results are compared with each other and some former results by calculating discrete root mean square and maximum error norms in each case. A matrix stability analysis is also performed by determining eigenvalues of the coefficient matrices numerically.

Numerical results show that differential quadrature methods based on cubic B‐splines generate acceptable solutions of nonlinear Burgers' equation. Constructing hybrid algorithms containing various basis to determine the weighting coefficients for higher order derivative approximations is also possible.

Nonlinear Burgers' equation is solved by cubic B‐spline differential quadrature methods.

This paper aims to present a numerical solution of non‐linear Burger's equation using differential quadrature method based on sinc functions.

Sinc Differential Quadrature Method is used for space discretization and four stage Runge‐Kutta algorithm is used for time discretization. A rate of convergency analysis is also performed for shock‐like solution. Numerical stability analysis is performed.

Sinc Differential Quadrature Method generates more accurate solutions of Burgers' equation when compared with the other methods.

This combination, Sinc Differential Quadrature and Runge‐Kutta of order four, has not been used to obtain numerical solutions of Burgers' equation.

Cubic B‐spline differential quadrature methods have been introduced. As test problems, two different solutions of advection‐diffusion equation are chosen. The first test problem, the transportion of an initial concentration, and the second one, the distribution of an initial pulse, are simulated. The purpose of this paper is to simulate the test problems.

The cubic B‐spline functions are chosen as test functions in order to construct the differential quadrature method. The error between the numerical solutions and analytical solutions are measured using various error norms.

The cubic B‐spline differential quadrature methods have produced acceptable solution for advection‐diffusion equation.

The advection‐diffusion equation has never been solved by any differential quadrature method based on cubic B‐splines.

The purpose of this study is to investigate the energy–growth linkage in sub-Saharan Africa (SSA), with emphasis on real sectors’ contribution to aggregate growth using dynamic panel estimation techniques that are practically and conceptually superior to the static models.

Dynamic panel econometric techniques pooled mean group, mean group and dynamic fixed effect were used to investigate the linkage among energy consumption, real sector value added and economic growth from 1967 to 2016 in 48 SSA countries.

A strong empirical evidence in favor of energy dependence and growth hypothesis in the investigated SSA countries was found. The finding that real sector value added and overall growth rate adjust reasonably to the shocks and dynamics of the energy consumption variables makes energy consumption an enabler for growth. This indicates that well thought-out and implemented energy development policy will not only increase energy consumption but also elicit multi-sectoral growth while addressing the obvious energy deficiency in the SSA region.

It is also important to note the policy implications of the high adjustment profiles indicated by the error correction representations. All the speeds of adjustment of the three models denominated in time are slightly above a year and are all within predictable limits (they fall below unity or 100%). We found that when agriculture value added, manufacturing value added and overall economic growth rate in our SSA panel estimation exceed equilibrium levels as a result of deviations arising from energy related variables, downward adjustments at 66%, 62% and 78% per year, respectively, take place.

The study indicates that well thought-out and implemented energy development policy will not only increase energy consumption but also elicit multi-sectoral growth while addressing the obvious energy deficiency in the SSA region.

Much as this study has made some addition to the literature on energy-growth nexus in the SSA region, which undoubtedly is an unveiling of economic forces in a collection of developing and energy deficient economies, it will be of great research significance if the form and style of this study is adopted for other economic blocs in the shapes and sizes of the SSA region.

This study ensured currency of data, novelty of approach and disaggregated energy consumption into emerging sources, traditional sources and geographical access.

The 17 December 2004 was a turning point in both Turkish and European history: The European Council followed the European Commission's recommendation and approved the opening of accession negotiations with Turkey, which commenced on 3 October 2005. The goal of accession to the European Union (EU) has become one of the main driving forces for broadly defined legal, political, economic, and financial reforms in Turkey.²