Modified Euler
Modified Euler ¶ A first order diffarential equation can be written as d y d x = f ( x , y ) " role="presentation"> d y d x = f ( x , y ) d y d x = f ( x , y ) It is given at x = x 0 " role="presentation" style="font-size: 119%; position: relative;"> x = x 0 x = x 0 , y = y 0 " role="presentation" style="font-size: 119%; position: relative;"> y = y 0 y = y 0 . So the next value of y " role="presentation" style="font-size: 119%; position: relative;"> y y i.e, y 1 " role="presentation" style="font-size: 119%; position: relative;"> y 1 y 1 is given by (1) y 1 = y 0 + ∫ x 0 x 1 d y d x d x = y 0 + ∫ x 0 x 1 f ( x , y ) d x " role="presentation"> y 1 = y 0 + ∫ x 1 x 0 d y d x d x = y 0 + ∫ x 1 x 0 f ( x , y ) d x (1) (1) y 1 = y 0 + ∫ x 0 x 1 d y d x d x = y 0 + ∫ x 0 x 1 f ( x , y ) d x Now the integral can be...
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