Finite Difference Method of solving (Second Order ODE) Initial Value Problem(IVP). Application

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Rajkishor Patra (M.Sc Jadavpur University)
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Finite Difference Method of solving (Second Order ODE) Initial Value Problem(IVP). Application.

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Second degree polynomial passes through (0,5),(2,7),(4,17),(6,35) is.👇
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Prove that u_0+x/1!u_1+x^2/2!+u_2+...=e^x[u_0+x∆u_0+x^2/2!∆^2u_0+...].👇
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Prove that u_0+n_c_1u_1x+n_c_2u_3x^3+...=(1+x)^nu_0+(1+x)^(n-1)x∆u_0+(1+x)^(n-2)x^2∆^2u_0+...👇
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Show that Summation x=0 to n=(n+1)_C_1 u_0+(n+1)_C_2∆ u_0+(n+1)_C_3∆^2 u_0+...+∆^nu_0 and hence find 1^3+2^3+....+n^3.👇
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Prove of ∆^(n+1)f(x)=h^(n+1)f^(n+1)(x) if h is very small. With explanation.👇
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3rd Lecture (Part -B)of finite Difference.
Definition of shift Operator and Central difference averaging and derivation inter relation.👇
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3rd Lecture (Part -A)of finite Difference.
Definition of shift Operator and Central difference averaging and derivation inter relation.👇
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2nd Lecture of finite Difference.Shift Operator and Central difference averaging and derivation inter relation.👇
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1st Lecture of finite Difference.
Definition of forward and backward difference and derivation inter relation.👇
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