Explanation Given: The system is, x ′ 1 = − ( 0.1 ) x 1 x 2 ; x 1 ( 0 ) = 10 x ′ 2 = − x 1 ; x 2 ( 0 ) = 15 Here, x 1 and x 2 are the strengths of guerrilla and conventional troops, respectively. Approach: The classical fourth-order Runge-Kutta method is x 1 ; n + 1 = x 1 ; n + 1 6 ( k 1 + 2 k 2 + 2 k 3 + k 4 ) ... ( 1 ) x 2 ; n + 1 = x 2 ; n + 1 6 ( l 1 + 2 l 2 + 2 l 3 + l 4 ) ... ( 2 ) Here, k 1 = h f ( t n , x 1 ; n , x 2 ; n ) l 1 = h g ( t n , x 1 ; n , x 2 ; n ) k 2 = h f ( t n + h 2 , x 1 ; n + k 1 2 , x 2 ; n + l 1 2 ) l 2 = h g ( t n + h 2 , x 1 ; n + k 1 2 , x 2 ; n + l 1 2 ) k 3 = h f ( t n + h 2 , x 1 ; n + k 2 2 , x 2 ; n + l 2 2 ) l 3 = h g ( t n + h 2 , x 1 ; n + k 2 2 , x 2 ; n + l 2 2 ) k 4 = h f ( t n + 1 , x 1 ; n + k 3 , x 2 ; n + l 3 ) l 4 = h g ( t n + 1 , x 1 ; n + k 3 , x 2 ; n + l 3 ) Calculation: Consider, h = 0.1 f ( t n , x 1 ; n , x 2 ; n ) = x ′ 1 = − ( 0.1 ) x 1 x 2 g ( t n , x 1 ; n , x 2 ; n ) = x ′ 2 = − x 1 The system of differential equation is not explicitly depended on t , as there is no term of t in the equation

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Chapter 5.3, Problem 18E

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The winner of the conflict among the conventional troops or the guerrilla combat.

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Chapter 5.3, Problem 17E

Chapter 5.3, Problem 19E

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The winner of the conflict among the conventional troops or the guerrilla combat.

Solution Summary: The author explains the classical fourth-order Runge-Kutta method of determining the winner of the conflict between the conventional troops or the guerrilla combat.

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The winner of the conflict among the conventional troops or the guerrilla combat.

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