John Wahome | Laikipia University (original) (raw)
Papers by John Wahome
The two dimensional coupled Burgers equations constitute an appropriate model for developing comp... more The two dimensional coupled Burgers equations constitute an appropriate model for developing computational algorithms, for solving the incompressible Navier-Stokes equations. Moreover, they are generally used as transport equations because they model a number of fluid flow phenomena, for example, the transport of a pollutant whose concentrations are u and v in a moving fluid in the x and y directions respectively. In this paper, we develop a new scheme known as the modified Crank-Nicolson (C-N) scheme from the Crank-Nicolson scheme by increasing the number of time levels from two to three. This is done by taking the average of the three adjacent grid points in time before the discretizing in space (i.e., ui, j n + 1 , uni , j, and ui, j n – 1). The modified C-N is implicit and produces excellent results that are comparable with those of the C-N scheme. L1 error analysis is carried out and shows that the scheme is second order convergent in space and time and the convergent rate is f...
Applied Mathematical Sciences, 2014
European Journal of Economic and Financial Research
The Government of Kenya through the Finance Act 2015 introduced a simplified rental income tax. T... more The Government of Kenya through the Finance Act 2015 introduced a simplified rental income tax. This is a monthly tax payable by a resident person for rental income earned from use or occupation of residential property. Upon the gazettement of the Income Tax (Residential Rental Income Tax) Regulations, 2016, the Kenya Revenue Authority embarked on an aggressive campaign to enlist landlords into the Monthly Rental Income Tax regime. However, the Economic Survey 2021 showed that the country’s revenue collecting agency KRA was not able to meet revenue targets as set by the National Treasury. Comparison of National Government Budget Estimates with Actual Out – turns for the fiscal years 2017/2018 and 2018/2019 showed that KRA missed the Budgeted Ordinary Revenue targets by Kshs.128.7 Billion and Kshs.90.1 Billion respectively. Property taxes including rental income tax are part of the ordinary revenue collected by the tax authority. The objective of the study was to investigate the infl...
During heavy rains, open channels are prone to being overrun with storm water. Since the velocity... more During heavy rains, open channels are prone to being overrun with storm water. Since the velocity of a flowing fluid increases with depth, sudden overflows may cause velocities to exceed certain limits. This damages the channel by scouring. On the other hand, siltation of suspended matter occurs in sluggish flow. Channel dimensions and John Wahome et al. 184 shapes must minimize cost and maximize discharge in normal seasons, while regulating the discharge to minimize velocity fluctuations during overflow. Depending on the designer's objectives, channel design involves numerous parameters, including the characteristics of construction materials and earthwork. Traditional methods such as Lagrange multipliers, sequential quadratic programming (SQP), differential evolution algorithm (DEA), genetic algorithms, ant-colony optimization, and lately, meta-heuristic algorithms are often used to minimize a cost function subject to channel cross-section. In this paper, using only the mathematical hydraulic efficiency criterion (other factors assumed optimum), a direct integro-differential technique is applied to determine the optimum triangular channel design that additionally minimizes velocity fluctuations during excessive discharge. The triangular channel is treated as a special case of a trapezoidal channel.
In open channels, fluid velocity increases with depth of flow. Sewers are particularly susceptibl... more In open channels, fluid velocity increases with depth of flow. Sewers are particularly susceptible to overwhelming storm water velocities during rains. When flow velocities exceed a certain threshold, damage of channel by scouring may result, or, conversely, siltation of suspended matter. Channel design must optimize dimensions and shapes which both minimize cost, maximizing discharge in normal seasons and regulate the discharge to minimize velocity fluctuations during overflow. Depending on the designer's objectives, channel design involves numerous parameters, including the characteristics of construction materials and earthwork. Traditional methods such as Langrage multipli-ers, Sequential Quadratic Programming (SQP), Differential Evolution Algorithm (DEA), genetic algorithms, ant-colony optimization, and lately, meta-heuristic algorithms are often used to minimize a cost function subject to channel cross-section. In this paper, using only the mathematical hydraulic efficiency criterion (other factors assumed optimum), a direct integro-differential technique is applied to determine the optimum trapezoidal channel design that additionally minimizes velocity fluctuations during excessive discharge.
The two dimensional coupled Burgers equations constitute an appropriate model for developing comp... more The two dimensional coupled Burgers equations constitute an appropriate model for developing computational algorithms, for solving the incompressible Navier-Stokes equations. Moreover, they are generally used as transport equations because they model a number of fluid flow phenomena, for example, the transport of a pollutant whose concentrations are u and v in a moving fluid in the x and y directions respectively. In this paper, we develop a new scheme known as the modified Crank-Nicolson (C-N) scheme from the Crank-Nicolson scheme by increasing the number of time levels from two to three. This is done by taking the average of the three adjacent grid points in time before the discretizing in space (i.e., ui, j n + 1 , uni , j, and ui, j n – 1). The modified C-N is implicit and produces excellent results that are comparable with those of the C-N scheme. L1 error analysis is carried out and shows that the scheme is second order convergent in space and time and the convergent rate is f...
Applied Mathematical Sciences, 2014
European Journal of Economic and Financial Research
The Government of Kenya through the Finance Act 2015 introduced a simplified rental income tax. T... more The Government of Kenya through the Finance Act 2015 introduced a simplified rental income tax. This is a monthly tax payable by a resident person for rental income earned from use or occupation of residential property. Upon the gazettement of the Income Tax (Residential Rental Income Tax) Regulations, 2016, the Kenya Revenue Authority embarked on an aggressive campaign to enlist landlords into the Monthly Rental Income Tax regime. However, the Economic Survey 2021 showed that the country’s revenue collecting agency KRA was not able to meet revenue targets as set by the National Treasury. Comparison of National Government Budget Estimates with Actual Out – turns for the fiscal years 2017/2018 and 2018/2019 showed that KRA missed the Budgeted Ordinary Revenue targets by Kshs.128.7 Billion and Kshs.90.1 Billion respectively. Property taxes including rental income tax are part of the ordinary revenue collected by the tax authority. The objective of the study was to investigate the infl...
During heavy rains, open channels are prone to being overrun with storm water. Since the velocity... more During heavy rains, open channels are prone to being overrun with storm water. Since the velocity of a flowing fluid increases with depth, sudden overflows may cause velocities to exceed certain limits. This damages the channel by scouring. On the other hand, siltation of suspended matter occurs in sluggish flow. Channel dimensions and John Wahome et al. 184 shapes must minimize cost and maximize discharge in normal seasons, while regulating the discharge to minimize velocity fluctuations during overflow. Depending on the designer's objectives, channel design involves numerous parameters, including the characteristics of construction materials and earthwork. Traditional methods such as Lagrange multipliers, sequential quadratic programming (SQP), differential evolution algorithm (DEA), genetic algorithms, ant-colony optimization, and lately, meta-heuristic algorithms are often used to minimize a cost function subject to channel cross-section. In this paper, using only the mathematical hydraulic efficiency criterion (other factors assumed optimum), a direct integro-differential technique is applied to determine the optimum triangular channel design that additionally minimizes velocity fluctuations during excessive discharge. The triangular channel is treated as a special case of a trapezoidal channel.
In open channels, fluid velocity increases with depth of flow. Sewers are particularly susceptibl... more In open channels, fluid velocity increases with depth of flow. Sewers are particularly susceptible to overwhelming storm water velocities during rains. When flow velocities exceed a certain threshold, damage of channel by scouring may result, or, conversely, siltation of suspended matter. Channel design must optimize dimensions and shapes which both minimize cost, maximizing discharge in normal seasons and regulate the discharge to minimize velocity fluctuations during overflow. Depending on the designer's objectives, channel design involves numerous parameters, including the characteristics of construction materials and earthwork. Traditional methods such as Langrage multipli-ers, Sequential Quadratic Programming (SQP), Differential Evolution Algorithm (DEA), genetic algorithms, ant-colony optimization, and lately, meta-heuristic algorithms are often used to minimize a cost function subject to channel cross-section. In this paper, using only the mathematical hydraulic efficiency criterion (other factors assumed optimum), a direct integro-differential technique is applied to determine the optimum trapezoidal channel design that additionally minimizes velocity fluctuations during excessive discharge.